Question

A circuit, having a resistance of 4.0 Ω with an inductance of 0.5 H and a variable capacitance in series, is connected across a 100 V, 50 Hz supply. Calculate: the capacitance required to attain resonance

Answer 1

The capacitance required to attain resonance in the circuit is 3.18 μF.

Step-by-step explanation:

To calculate the capacitance required to attain resonance in the given circuit, we need to use the formula for resonant frequency:

fr = 1 / (2π√(LC))

Given values: Resistance (R) = 4.0 Ω, Inductance (L) = 0.5 H. We need to find the capacitance (C).

Substituting these values in the formula, we have:

50 = 1 / (2π√(0.5C))

Simplifying the equation and solving for C:

C = (1 / (4π² × L × f²)) = (1 / (4π² × 0.5 × 50²)) = 3.18 μF

Therefore, the required capacitance to attain resonance in the circuit is 3.18 μF.