The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The resistance R is slowly increasing as the resistor heats up. Use Ohm’s Law, V = IR, to find how the current I is changing at the moment when R = 400 Ω, I = 0.08 A, dV/dt = −0.01 V/s, and dR/dt = 0.03 Ω/s.
To find: The rate of change of I when and .
The Ohm’s Law is V=IR where V is voltage, I is current and R is resistance.
The values of and .
“Suppose that is a differentiable function of and , where are both differentiable functions of then, is differentiable function of and ”.
The Ohm’s Law V = IR can be written as, .
By using chain rule, obtain the value of .
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