in amps. a constant voltage of 77 volts is put across a resistance that is increasing at a rate of 0.20.2 ohms per second when the resistance is 55 ohms. at what rate is the current changing?

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09-12-2022
Physics

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in amps. a constant voltage of 77 volts is put across a resistance that is increasing at a rate of 0.20.2 ohms per second when the resistance is 55 ohms. at what rate is the current changing?

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-15T11:50:23-05:00

A constant voltage of 77 volts is put across a resistance that is increasing at a rate of 0.202 ohms per second when the resistance is 55 ohms. The current is changing at a rate of 0.0051amps per sec

Given voltage (V) = 77v

Resistance (R) = 55ohms

The relation among voltage (V), resistance (R) and current (I) is given as

I =V/R

The increasing rate of resistance is = dR/dt = 0.2ohms per second

By derivating the current to get rate of change in current

dI/dt = Vxd/dt(1/R) [ Because V is a constant ]

dI/dt = V x d/dt(R −1)

dI/dt = V(-1/R^2 x dR/dt) = 77x (-1/55x55) x 0.202 = -0.005amp per second

Hence the current is changing at a rate of 0.0051amps per sec

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