Question

A 360 -Hz source of emf is connected in a circuit consisting of a capacitor, a \(25-\mathrm{mH}\) inductor, and an \(0.80-\Omega\) resistor. For the current and the voltage to be in phase, what should the value of \(C\) be?

Short answer

Answer: The capacitance (C) for the current and voltage to be in phase in the given RLC circuit is approximately 1.246 * 10^-6 F or 1.246 μF.

Step-by-step solution

Given values and formulae

We are given the following values: - Frequency (f) = 360 Hz - Inductor (L) = 25 mH = 0.025 H - Resistor (R) = 0.80 Ω We need to find the capacitance (C) for the current and voltage to be in phase. Formulae we need: 1. Inductive reactance (XL) = 2 * π * f * L 2. Capacitive reactance (XC) = 1 / (2 * π * f * C)

Calculate inductive reactance (XL)

Calculate inductive reactance (XL) using the formula: XL = 2 * π * f * L = 2 * π * 360 * 0.025 XL ≈ 56.55 Ω

Equate inductive and capacitive reactances

In the case when the current and voltage are in phase, inductive reactance will be equal to capacitive reactance (XL = XC), so we get: 56.55 = 1 / (2 * π * 360 * C)

Solve for capacitance (C)

Now rearrange the equation to solve for C: C = 1 / (2 * π * 360 * 56.55) C ≈ 1.246 * 10^-6 F So, the value of the capacitance C should be approximately 1.246 * 10^-6 F or 1.246 μF for the current and voltage to be in phase in the given RLC circuit.