In a simple electric circuit, Ohm\'s law states that V = IR, where V is the volt

Question

In a simple electric circuit, Ohm's law states that V = IR, where V is the voltage in volts, l is the current in amperes, and R is the resistance in ohms. Assume that, as the battery wears out, the voltage decreases at 0.01 volts per second and, as the resistor heats up, the resistance is increasing at 0.03 ohms per second. When the resistance is 100 ohms and the current is 0.04 amperes, at what rate is the current changing? __________ amperes per second The radius of a right circular cone is increasing at a rate of 2 inches per second and its height is decreasing at a rate of 2 inches per second. At what rate is the volume of the cone changing when the radius is 10 inches and the height is 20 inches? _____ cubic inches per second

Explanation / Answer

5.)

V=IR

I=0.04 ,R=100

V=0.04*100

V=4 volts

given V=IR,dV/dt =-0.01 ,dR/dt=0.03

=>I=V/R

differentiate with respect to time t

=>dI/dt=[(dV/dt*R)-(V*dR/dt)]/R2

=>dI/dt=[(-0.01*100)-(4*0.03)]/1002

=>dI/dt=-0.000112

current is decreasing at 0.000112 amperes per second

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6)

dr/dt=2 , dh/dt=-2 ,r=10 , h=20

volume V=(1/3)r2h

dV/dt=(1/3)[(2r(dr/dt)h) +(r2(dh/dt))]

dV/dt=(1/3)[(2*10*2*20) +(102(-2))]

dV/dt=(1/3)[800-200]

dV/dt=200

volume is increasing at 200 cubic inches per second

volume is increasing at 628.32 cubic inches per second

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