Suppose that the voltage across the resistor is held constant at 40 volts. If the resistance is steadily decreasing at a rate of 0.2 ohms per second, at what rate is the current changing at the moment that the resistor reaches 5 ohms?

The current is increasing at a rate of 0.32 ampere per second.

Explanation:

The voltage of the resistor is modelled after Ohm's Law, which states that voltage is directly proportional to current:

(1)

Where:

- Voltage, measured in volts.

- Current, measured in amperes.

- Resistance, measured in ohms.

An expression for the rate of change in voltage is found by Differential Calculus:

(2)

Where:

- Rate of change in voltage, measured in volts per second.

- Rate of change in current, measured in amperes per second.

- Rate of change in resistance, measured in ohms per second.

If we know that , , and , then the rate of change in current is:

(3)

The current is increasing at a rate of 0.32 ampere per second.