Calculus 3: Finding Current Rate of Change in Electric Circuits Using Chain Rule

[krtica]

In a simple electric circuit, Ohm's law states that V = IR, where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms. Assume that, as the battery wears out, the voltage decreases at 0.03 volts per second and, as the resistor heats up, the resistance is increasing at 0.02 ohms per second. When the resistance is 400 ohms and the current is 0.04 amperes, at what rate is the current changing?

Would I differentiate implicitly with respect to the current, I?

 

[tt2348]

start out by differentiating both sides with respect to time, try using the product rule on the right hand side.

 

[Mark44]

To expand on what tt2348 said, you would NOT differentiate with respect to I. The question is "at what rate is the current changing?" This implies that you should take the derivative of I with respect to something (an excellent candidate would be t), not differentiate with respect to I.

IOW, they're asking for dI/dt, the time rate of change of current.