Question

31.4 the series rlc circuit
an rl series circuit is connected to an ac generator with a maximum emf of 25 v. if the maximum potential difference across the resistor is 20.0 v, then the maximum potential difference across the inductor is
32 v.
5.0 v.
15 v.
2.5 v.
45 v.

Explanation:

Step1: Apply the formula for an RL series circuit

In an RL series circuit, the maximum emf \( \mathcal{E}_{max}\) is related to the maximum potential differences across the resistor \( V_{R,max}\) and inductor \( V_{L,max}\) by the formula \( \mathcal{E}_{max}=\sqrt{V_{R,max}^{2}+V_{L,max}^{2}}\).

Step2: Rearrange the formula to solve for \( V_{L,max}\)

We can rewrite the formula as \( V_{L,max}=\sqrt{\mathcal{E}_{max}^{2}-V_{R,max}^{2}}\).
Substitute \( \mathcal{E}_{max} = 25\space V\) and \( V_{R,max}=20.0\space V\) into the formula:

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Answer:

15 V.