The voltage, V, in volts across a circuit is given by Ohm\'s Law: V = IR, where

Question

The voltage, V, in volts across a circuit is given by Ohm's Law: V = IR, where I is the current (in amps) flowing through the circuit and R is the resistance (in ohms). If we place two circuits with resistance R1 and R2, in parallel, then their combined resistance, R, is given by: 1/R = (1/R1)+(1/R2). Supposed the current is 3 amps and increasing at 10^-2 amp/sec and R1 is 5 ohms and increasing at 0.5 ohm/sec, while R2 is 12 ohms and decreasing at 0.1 ohm/sec. Calculate the rate at which the voltage is changing. Rate = ? volts/sec. Show all steps and round the answer to three decimal places.

Explanation / Answer

V=IR; dV/dt=dI/dt*R+IdR/dt; dR/dt=1/R1(dR1/dt)+1/R2(dR2/dt); =1.3/12; dV/dt=60/17(10^-2)+3(1.3/12)=0.360 volts/sec;

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