Find the charge q ( t ) flowing through a device if the current is: (a) i ( t ) = 3 A, q (0) = 1 C (b) i ( t ) = (2 t + 5) mA, q (0) = 0 (c) i ( t ) = 20 cos(10 t + π/6) μ A, q (0) = 2 μ C (d) i ( t ) = 10 e ‒30 t sin 40 t A, q (0) = 0

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Answer 1

Textbook Question

Chapter 1, Problem 3P

Find the charge q(t) flowing through a device if the current is:

(a) i(t) = 3 A, q(0) = 1 C
(b) i(t) = (2t + 5) mA, q(0) = 0
(c) i(t) = 20 cos(10t + π/6) μA, q(0) = 2μC
(d) i(t) = 10e^‒30t sin 40t A, q (0) = 0

(a)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=3 A, and q(0)=1 C.

Answer to Problem 3P

The charge q(t) flowing through the device is (3t+1) C_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 3 A.

The charge at initial state [q(0)] is 1 C.

Formula used:

Write the expression for charge entering to the device as follows:

q(t)=∫i(t)dt+q(0) (1)

Here,

i(t) is the current through the device, and

q(0) is the charge at initial state.

Calculation:

Substitute 3 A for i(t) and 1 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫(3 A)dt+1 C=3t C+1 C=(3t+1) C

Conclusion:

Thus, the charge q(t) flowing through the device is (3t+1) C_.

(b)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=(2t+5) mA, and q(0)=0 mC.

Answer to Problem 3P

The charge q(t) flowing through the device is (t2+5t) mC_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is (2t+5) mA.

The charge at initial state [q(0)] is 0 mC.

Calculation:

Substitute (2t+5) mA for i(t) and 0 mC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[(2t+5) mA]dt+0 mC=∫[(2t) mA]dt+∫[(5) mA]dt=2(t22) mC+5t mC=(t2+5t) mC

Conclusion:

Thus, the charge q(t) flowing through the device is (t2+5t) mC_.

(c)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=20cos(10t+π/6) μA, and q(0)=2 μC.

Answer to Problem 3P

The charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 20cos(10t+π/6) μA.

The charge at initial state [q(0)] is 2 μC.

Calculation:

Substitute 20cos(10t+π/6) μA for i(t) and 2 μC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[20cos(10t+π/6) μA]dt+2 μC=20sin(10t+π/6)10 μC+2 μC {∵∫cos(at)dt=sin(at)a}=2sin(10t+π/6) μC+2 μC=2[sin(10t+π/6)+1] μC

Conclusion:

Thus, the charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

(d)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=10e−30tsin(40t) A, and q(0)=0 C.

Answer to Problem 3P

The cha charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 10e−30tsin(40t) A.

The charge at initial state [q(0)] is 0 C.

Calculation:

Substitute 10e−30tsin(40t) A for i(t) and 0 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[10e−30tsin(40t) A]dt+0 C=10{∫[e−30tsin(40t)]dt} C=10{e−30t[(−30)sin(40t)−40cos(40t)](−30)2+402+C} C {∵∫eatsin(bt)dt=eat[asin(bt)−bcos(bt)]a2+b2+C}=10{e−30t[−30sin(40t)−40cos(40t)]900+1600} C

Simplify the expression as follows:

q(t)=e−30t[−300sin(40t)2500−400cos(40t)2500] C=−e−30t[0.12sin(40t)+0.16cos(40t)] C

Conclusion:

Thus, the charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

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Answer 2

Textbook Question

Chapter 1, Problem 3P

Find the charge q(t) flowing through a device if the current is:

(a) i(t) = 3 A, q(0) = 1 C
(b) i(t) = (2t + 5) mA, q(0) = 0
(c) i(t) = 20 cos(10t + π/6) μA, q(0) = 2μC
(d) i(t) = 10e^‒30t sin 40t A, q (0) = 0

(a)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=3 A, and q(0)=1 C.

Answer to Problem 3P

The charge q(t) flowing through the device is (3t+1) C_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 3 A.

The charge at initial state [q(0)] is 1 C.

Formula used:

Write the expression for charge entering to the device as follows:

q(t)=∫i(t)dt+q(0) (1)

Here,

i(t) is the current through the device, and

q(0) is the charge at initial state.

Calculation:

Substitute 3 A for i(t) and 1 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫(3 A)dt+1 C=3t C+1 C=(3t+1) C

Conclusion:

Thus, the charge q(t) flowing through the device is (3t+1) C_.

(b)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=(2t+5) mA, and q(0)=0 mC.

Answer to Problem 3P

The charge q(t) flowing through the device is (t2+5t) mC_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is (2t+5) mA.

The charge at initial state [q(0)] is 0 mC.

Calculation:

Substitute (2t+5) mA for i(t) and 0 mC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[(2t+5) mA]dt+0 mC=∫[(2t) mA]dt+∫[(5) mA]dt=2(t22) mC+5t mC=(t2+5t) mC

Conclusion:

Thus, the charge q(t) flowing through the device is (t2+5t) mC_.

(c)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=20cos(10t+π/6) μA, and q(0)=2 μC.

Answer to Problem 3P

The charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 20cos(10t+π/6) μA.

The charge at initial state [q(0)] is 2 μC.

Calculation:

Substitute 20cos(10t+π/6) μA for i(t) and 2 μC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[20cos(10t+π/6) μA]dt+2 μC=20sin(10t+π/6)10 μC+2 μC {∵∫cos(at)dt=sin(at)a}=2sin(10t+π/6) μC+2 μC=2[sin(10t+π/6)+1] μC

Conclusion:

Thus, the charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

(d)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=10e−30tsin(40t) A, and q(0)=0 C.

Answer to Problem 3P

The cha charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 10e−30tsin(40t) A.

The charge at initial state [q(0)] is 0 C.

Calculation:

Substitute 10e−30tsin(40t) A for i(t) and 0 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[10e−30tsin(40t) A]dt+0 C=10{∫[e−30tsin(40t)]dt} C=10{e−30t[(−30)sin(40t)−40cos(40t)](−30)2+402+C} C {∵∫eatsin(bt)dt=eat[asin(bt)−bcos(bt)]a2+b2+C}=10{e−30t[−30sin(40t)−40cos(40t)]900+1600} C

Simplify the expression as follows:

q(t)=e−30t[−300sin(40t)2500−400cos(40t)2500] C=−e−30t[0.12sin(40t)+0.16cos(40t)] C

Conclusion:

Thus, the charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

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Answer 3

Textbook Question

Chapter 1, Problem 3P

Find the charge q(t) flowing through a device if the current is:

(a) i(t) = 3 A, q(0) = 1 C
(b) i(t) = (2t + 5) mA, q(0) = 0
(c) i(t) = 20 cos(10t + π/6) μA, q(0) = 2μC
(d) i(t) = 10e^‒30t sin 40t A, q (0) = 0

(a)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=3 A, and q(0)=1 C.

Answer to Problem 3P

The charge q(t) flowing through the device is (3t+1) C_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 3 A.

The charge at initial state [q(0)] is 1 C.

Formula used:

Write the expression for charge entering to the device as follows:

q(t)=∫i(t)dt+q(0) (1)

Here,

i(t) is the current through the device, and

q(0) is the charge at initial state.

Calculation:

Substitute 3 A for i(t) and 1 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫(3 A)dt+1 C=3t C+1 C=(3t+1) C

Conclusion:

Thus, the charge q(t) flowing through the device is (3t+1) C_.

(b)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=(2t+5) mA, and q(0)=0 mC.

Answer to Problem 3P

The charge q(t) flowing through the device is (t2+5t) mC_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is (2t+5) mA.

The charge at initial state [q(0)] is 0 mC.

Calculation:

Substitute (2t+5) mA for i(t) and 0 mC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[(2t+5) mA]dt+0 mC=∫[(2t) mA]dt+∫[(5) mA]dt=2(t22) mC+5t mC=(t2+5t) mC

Conclusion:

Thus, the charge q(t) flowing through the device is (t2+5t) mC_.

(c)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=20cos(10t+π/6) μA, and q(0)=2 μC.

Answer to Problem 3P

The charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 20cos(10t+π/6) μA.

The charge at initial state [q(0)] is 2 μC.

Calculation:

Substitute 20cos(10t+π/6) μA for i(t) and 2 μC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[20cos(10t+π/6) μA]dt+2 μC=20sin(10t+π/6)10 μC+2 μC {∵∫cos(at)dt=sin(at)a}=2sin(10t+π/6) μC+2 μC=2[sin(10t+π/6)+1] μC

Conclusion:

Thus, the charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

(d)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=10e−30tsin(40t) A, and q(0)=0 C.

Answer to Problem 3P

The cha charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 10e−30tsin(40t) A.

The charge at initial state [q(0)] is 0 C.

Calculation:

Substitute 10e−30tsin(40t) A for i(t) and 0 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[10e−30tsin(40t) A]dt+0 C=10{∫[e−30tsin(40t)]dt} C=10{e−30t[(−30)sin(40t)−40cos(40t)](−30)2+402+C} C {∵∫eatsin(bt)dt=eat[asin(bt)−bcos(bt)]a2+b2+C}=10{e−30t[−30sin(40t)−40cos(40t)]900+1600} C

Simplify the expression as follows:

q(t)=e−30t[−300sin(40t)2500−400cos(40t)2500] C=−e−30t[0.12sin(40t)+0.16cos(40t)] C

Conclusion:

Thus, the charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

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Answer 4

Textbook Question

Chapter 1, Problem 3P

Find the charge q(t) flowing through a device if the current is:

(a) i(t) = 3 A, q(0) = 1 C
(b) i(t) = (2t + 5) mA, q(0) = 0
(c) i(t) = 20 cos(10t + π/6) μA, q(0) = 2μC
(d) i(t) = 10e^‒30t sin 40t A, q (0) = 0

(a)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=3 A, and q(0)=1 C.

Answer to Problem 3P

The charge q(t) flowing through the device is (3t+1) C_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 3 A.

The charge at initial state [q(0)] is 1 C.

Formula used:

Write the expression for charge entering to the device as follows:

q(t)=∫i(t)dt+q(0) (1)

Here,

i(t) is the current through the device, and

q(0) is the charge at initial state.

Calculation:

Substitute 3 A for i(t) and 1 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫(3 A)dt+1 C=3t C+1 C=(3t+1) C

Conclusion:

Thus, the charge q(t) flowing through the device is (3t+1) C_.

(b)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=(2t+5) mA, and q(0)=0 mC.

Answer to Problem 3P

The charge q(t) flowing through the device is (t2+5t) mC_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is (2t+5) mA.

The charge at initial state [q(0)] is 0 mC.

Calculation:

Substitute (2t+5) mA for i(t) and 0 mC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[(2t+5) mA]dt+0 mC=∫[(2t) mA]dt+∫[(5) mA]dt=2(t22) mC+5t mC=(t2+5t) mC

Conclusion:

Thus, the charge q(t) flowing through the device is (t2+5t) mC_.

(c)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=20cos(10t+π/6) μA, and q(0)=2 μC.

Answer to Problem 3P

The charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 20cos(10t+π/6) μA.

The charge at initial state [q(0)] is 2 μC.

Calculation:

Substitute 20cos(10t+π/6) μA for i(t) and 2 μC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[20cos(10t+π/6) μA]dt+2 μC=20sin(10t+π/6)10 μC+2 μC {∵∫cos(at)dt=sin(at)a}=2sin(10t+π/6) μC+2 μC=2[sin(10t+π/6)+1] μC

Conclusion:

Thus, the charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

(d)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=10e−30tsin(40t) A, and q(0)=0 C.

Answer to Problem 3P

The cha charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 10e−30tsin(40t) A.

The charge at initial state [q(0)] is 0 C.

Calculation:

Substitute 10e−30tsin(40t) A for i(t) and 0 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[10e−30tsin(40t) A]dt+0 C=10{∫[e−30tsin(40t)]dt} C=10{e−30t[(−30)sin(40t)−40cos(40t)](−30)2+402+C} C {∵∫eatsin(bt)dt=eat[asin(bt)−bcos(bt)]a2+b2+C}=10{e−30t[−30sin(40t)−40cos(40t)]900+1600} C

Simplify the expression as follows:

q(t)=e−30t[−300sin(40t)2500−400cos(40t)2500] C=−e−30t[0.12sin(40t)+0.16cos(40t)] C

Conclusion:

Thus, the charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=3 A, and q(0)=1 C.

Answer to Problem 3P

The charge q(t) flowing through the device is (3t+1) C_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 3 A.

The charge at initial state [q(0)] is 1 C.

Formula used:

Write the expression for charge entering to the device as follows:

q(t)=∫i(t)dt+q(0) (1)

Here,

i(t) is the current through the device, and

q(0) is the charge at initial state.

Calculation:

Substitute 3 A for i(t) and 1 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫(3 A)dt+1 C=3t C+1 C=(3t+1) C

Conclusion:

Thus, the charge q(t) flowing through the device is (3t+1) C_.

(b)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=(2t+5) mA, and q(0)=0 mC.

Answer to Problem 3P

The charge q(t) flowing through the device is (t2+5t) mC_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is (2t+5) mA.

The charge at initial state [q(0)] is 0 mC.

Calculation:

Substitute (2t+5) mA for i(t) and 0 mC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[(2t+5) mA]dt+0 mC=∫[(2t) mA]dt+∫[(5) mA]dt=2(t22) mC+5t mC=(t2+5t) mC

Conclusion:

Thus, the charge q(t) flowing through the device is (t2+5t) mC_.

(c)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=20cos(10t+π/6) μA, and q(0)=2 μC.

Answer to Problem 3P

The charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 20cos(10t+π/6) μA.

The charge at initial state [q(0)] is 2 μC.

Calculation:

Substitute 20cos(10t+π/6) μA for i(t) and 2 μC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[20cos(10t+π/6) μA]dt+2 μC=20sin(10t+π/6)10 μC+2 μC {∵∫cos(at)dt=sin(at)a}=2sin(10t+π/6) μC+2 μC=2[sin(10t+π/6)+1] μC

Conclusion:

Thus, the charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

(d)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=10e−30tsin(40t) A, and q(0)=0 C.

Answer to Problem 3P

The cha charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 10e−30tsin(40t) A.

The charge at initial state [q(0)] is 0 C.

Calculation:

Substitute 10e−30tsin(40t) A for i(t) and 0 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[10e−30tsin(40t) A]dt+0 C=10{∫[e−30tsin(40t)]dt} C=10{e−30t[(−30)sin(40t)−40cos(40t)](−30)2+402+C} C {∵∫eatsin(bt)dt=eat[asin(bt)−bcos(bt)]a2+b2+C}=10{e−30t[−30sin(40t)−40cos(40t)]900+1600} C

Simplify the expression as follows:

q(t)=e−30t[−300sin(40t)2500−400cos(40t)2500] C=−e−30t[0.12sin(40t)+0.16cos(40t)] C

Conclusion:

Thus, the charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

Answer 8

(a)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=3 A, and q(0)=1 C.

Answer to Problem 3P

The charge q(t) flowing through the device is (3t+1) C_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 3 A.

The charge at initial state [q(0)] is 1 C.

Formula used:

Write the expression for charge entering to the device as follows:

q(t)=∫i(t)dt+q(0) (1)

Here,

i(t) is the current through the device, and

q(0) is the charge at initial state.

Calculation:

Substitute 3 A for i(t) and 1 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫(3 A)dt+1 C=3t C+1 C=(3t+1) C

Conclusion:

Thus, the charge q(t) flowing through the device is (3t+1) C_.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=3 A, and q(0)=1 C.

Answer 13

Answer to Problem 3P

The charge q(t) flowing through the device is (3t+1) C_.

Answer 14

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 3 A.

The charge at initial state [q(0)] is 1 C.

Formula used:

Write the expression for charge entering to the device as follows:

q(t)=∫i(t)dt+q(0) (1)

Here,

i(t) is the current through the device, and

q(0) is the charge at initial state.

Calculation:

Substitute 3 A for i(t) and 1 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫(3 A)dt+1 C=3t C+1 C=(3t+1) C

Conclusion:

Thus, the charge q(t) flowing through the device is (3t+1) C_.

Answer 15

(b)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=(2t+5) mA, and q(0)=0 mC.

Answer to Problem 3P

The charge q(t) flowing through the device is (t2+5t) mC_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is (2t+5) mA.

The charge at initial state [q(0)] is 0 mC.

Calculation:

Substitute (2t+5) mA for i(t) and 0 mC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[(2t+5) mA]dt+0 mC=∫[(2t) mA]dt+∫[(5) mA]dt=2(t22) mC+5t mC=(t2+5t) mC

Conclusion:

Thus, the charge q(t) flowing through the device is (t2+5t) mC_.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=(2t+5) mA, and q(0)=0 mC.

Answer 20

Answer to Problem 3P

The charge q(t) flowing through the device is (t2+5t) mC_.

Answer 21

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is (2t+5) mA.

The charge at initial state [q(0)] is 0 mC.

Calculation:

Substitute (2t+5) mA for i(t) and 0 mC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[(2t+5) mA]dt+0 mC=∫[(2t) mA]dt+∫[(5) mA]dt=2(t22) mC+5t mC=(t2+5t) mC

Conclusion:

Thus, the charge q(t) flowing through the device is (t2+5t) mC_.

Answer 22

(c)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=20cos(10t+π/6) μA, and q(0)=2 μC.

Answer to Problem 3P

The charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 20cos(10t+π/6) μA.

The charge at initial state [q(0)] is 2 μC.

Calculation:

Substitute 20cos(10t+π/6) μA for i(t) and 2 μC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[20cos(10t+π/6) μA]dt+2 μC=20sin(10t+π/6)10 μC+2 μC {∵∫cos(at)dt=sin(at)a}=2sin(10t+π/6) μC+2 μC=2[sin(10t+π/6)+1] μC

Conclusion:

Thus, the charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=20cos(10t+π/6) μA, and q(0)=2 μC.

Answer 27

Answer to Problem 3P

The charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

Answer 28

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 20cos(10t+π/6) μA.

The charge at initial state [q(0)] is 2 μC.

Calculation:

Substitute 20cos(10t+π/6) μA for i(t) and 2 μC for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[20cos(10t+π/6) μA]dt+2 μC=20sin(10t+π/6)10 μC+2 μC {∵∫cos(at)dt=sin(at)a}=2sin(10t+π/6) μC+2 μC=2[sin(10t+π/6)+1] μC

Conclusion:

Thus, the charge q(t) flowing through the device is 2[sin(10t+π/6)+1] μC_.

Answer 29

(d)

Expert Solution

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=10e−30tsin(40t) A, and q(0)=0 C.

Answer to Problem 3P

The cha charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 10e−30tsin(40t) A.

The charge at initial state [q(0)] is 0 C.

Calculation:

Substitute 10e−30tsin(40t) A for i(t) and 0 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[10e−30tsin(40t) A]dt+0 C=10{∫[e−30tsin(40t)]dt} C=10{e−30t[(−30)sin(40t)−40cos(40t)](−30)2+402+C} C {∵∫eatsin(bt)dt=eat[asin(bt)−bcos(bt)]a2+b2+C}=10{e−30t[−30sin(40t)−40cos(40t)]900+1600} C

Simplify the expression as follows:

q(t)=e−30t[−300sin(40t)2500−400cos(40t)2500] C=−e−30t[0.12sin(40t)+0.16cos(40t)] C

Conclusion:

Thus, the charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

Calculate the charge q(t) flowing through a device when the current is i(t)=10e−30tsin(40t) A, and q(0)=0 C.

Answer 34

Answer to Problem 3P

The cha charge q(t) flowing through the device is −e−30t[0.12sin(40t)+0.16cos(40t)] C_.

Answer 35

Explanation of Solution

Given data:

The current flowing through the device [i(t)] is 10e−30tsin(40t) A.

The charge at initial state [q(0)] is 0 C.

Calculation:

Substitute 10e−30tsin(40t) A for i(t) and 0 C for q(0) in equation (1) to obtain the charge flowing through the device as follows:

q(t)=∫[10e−30tsin(40t) A]dt+0 C=10{∫[e−30tsin(40t)]dt} C=10{e−30t[(−30)sin(40t)−40cos(40t)](−30)2+402+C} C {∵∫eatsin(bt)dt=eat[asin(bt)−bcos(bt)]a2+b2+C}=10{e−30t[−30sin(40t)−40cos(40t)]900+1600} C