A charge of #16 C# passes through a circuit every #12 s#. If the circuit can generate #9 W# of power, what is the circuit's resistance?

We can evaluate current as:

With your data:

Now, power is:

rearranging:

Use the formula P = VI and Ohm's Law (V = IR) to find resistance (R). R = P/I², where P is power and I is current. Calculate current (I) using Q = It. Then find resistance. R ≈ 5.0625 ohms.

To find the resistance of the circuit, we can use the formula for power in terms of current and resistance, which is ( P = I^2 R ), where ( P ) is power, ( I ) is current, and ( R ) is resistance. First, we need to find the current flowing through the circuit. Current can be calculated using the formula ( I = \frac{Q}{t} ), where ( Q ) is charge and ( t ) is time. Once we have the current, we can rearrange the power formula to solve for resistance, which gives us ( R = \frac{P}{I^2} ). Substituting the given values into these equations will give us the resistance of the circuit.