Question

Asked Oct 5, 2019

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Joules Law allows us to compute the power in a simple electric circuit: P=I^{2}R

a) Use the equation above to find an equation relating (dP/dt), (dI/dt), (dR/dt), I and R.

b) I have a circuit with a 400 ohm resistor. I increase the voltage at 20 Volts/s. When the voltage reaches 350 volts, how quickly is the Power in the circuit increasing? Include units in your answer. Note that 1 Watt is equivalent to 1 Volt^{2}/ohm. *Hint: you will need to use another equation relating voltage to current from the acticity in class. *

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Step 1

**Given information:**

Relation between P, I, R as:

P = I^{2}R

Resistance in the circuit (R) = 400 ohms

Rate of change of voltage (dV/dt) = 20 volts/s

Final voltage of the circuit (V) = 350 volts

Step 2

Part a:

In P = I^{2}R differentiate both the sides with time we get:

Step 3

We know, from ohms law...

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