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Chapter 1 Solutions (1)

# Chapter 1 Solutions (1) - Problem 1.7 Determine the current...

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Problem 1.7 Determine the current i ( t ) flowing through a resistor if the cumulative charge that has flowed through it up to time t is given by (a) q ( t ) = 3 . 6 t mC (b) q ( t ) = 5sin ( 377 t ) μ C (c) q ( t ) = 0 . 3 [ 1 e 0 . 4 t ] pC (d) q ( t ) = 0 . 2 t sin ( 120 π t ) nC Solution: (a) i ( t ) = dq dt = d dt ( 3 . 6 t × 10 3 ) = 3 . 6 × 10 3 = 3 . 6 (mA). (b) i ( t ) = dq dt = d dt [( 5sin377 t ) × 10 6 ] = 5 × 377 × 10 6 cos377 t = 1 . 885cos377 t (mA). (c) i ( t ) = dq dt = d dt [ 0 . 3 ( 1 e 0 . 4 t ) × 10 12 ] = 0 . 3 × 10 12 × ( 0 . 4 ) × ( e 0 . 4 t ) = 0 . 12 e 0 . 4 t (pA). (d) i ( t ) = dq dt = d dt [( 0 . 2 t sin120 π t ) × 10 9 ] = ( 0 . 2sin120 π t + 0 . 2 t × 120 π cos120 π t ) × 10 9 = 0 . 2sin120 π t + 75 . 4 t cos120 π t (nA) .

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Problem 1.8 Determine the current i ( t ) flowing through a certain device if the cumulative charge that has flowed through it up to time t is given by (a) q ( t ) = 0 . 45 t 3 μ C (b) q ( t ) = 12sin 2 ( 800 π t ) mC (c) q ( t ) = 3 . 2sin ( 377 t ) cos ( 377 t ) pC (d) q ( t ) = 1 . 7 t [ 1 e 1 . 2 t ] nC Solution: (a) i ( t ) = dq dt = d dt [ 0 . 45 t 3 × 10 6 ] = 0 . 45 × 3 t 2 × 10 6 = 1 . 35 t 2 ( μ A) .
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Chapter 1 Solutions (1) - Problem 1.7 Determine the current...

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