A voltage V (volts) across a resistance R (ohms) generates a current 1 (amps) ac

Question

A voltage V (volts) across a resistance R (ohms) generates a current 1 (amps) according to I =-. (a) Suppose voltage is constant, but resistance is changing with time. Which of the following could be used to find the rate at which the current changes with time? V dR dI dt R2 dt dI dt R dt dt dl dR dI dR R2 dt R dt (b) If a constant voltage of 9 volts is put across a resistance that is decreasing at a rate of 0.4 ohms per second when the resistance is 5 ohms, at what rate is the current changing? Round your answer to 3 decimal places amps per sec (c) Is the current in part (b) increasing or decreasing? Increasing Decreasing

Explanation / Answer

I = V/R

differentiation w.r.t 't'

di/dt = V*(-1/R^2)*dR/dt

di/dt = -(V/R^2)*(dR/dt)

Correct option is A.

2.

when V = 9 V, R = 5 ohm and dR/dt = 0.4 ohm/sec

di/dt = -(9/5^2)*0.4 = -0.144 Amp/sec

3.

Since di/dt < 0, current is decreasing.

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