Question

An inductor with inductance \(L\) is connected to an AC power source that supplies \(V_{\mathrm{emf}}=21.5 \mathrm{~V}\) at \(f=797 \mathrm{~Hz}\). If the maximum current in the circuit is to be \(0.1528 \mathrm{~A},\) what should the value of \(L\) be?

Short answer

Answer: The value of the inductor (L) is approximately 0.028 H.

Step-by-step solution

Find the angular frequency

To find the angular frequency (ω), we use the formula: ω = 2πf From the given problem, f = 797 Hz. Plug in the values for the frequency and calculate ω: ω = 2π(797) ≈ 5007.44 rad/s

Rewrite Ohm's Law for AC circuits

In AC circuits, we use Ohm's law in terms of impedance (Z) rather than resistance (R). The formula looks like this: V_emf = I_max * Z From the given problem, V_emf = 21.5 V and I_max = 0.1528 A. Plug in the values for the voltage and current: 21.5 = 0.1528 * Z Z ≈ 140.64 Ω (approximated)

Write the impedance formula for the inductor

The impedance (Z) of an inductor is given by the formula: Z = ω * L

Solve for the inductance (L)

We now have the values for ω and Z. Plug in the values and solve for L: 140.64 ≈ 5007.44 * L L ≈ 0.028 H So, the inductance (L) of the inductor should be approximately 0.028 H.