A 60 μF capacitor is connected to a 110 V, 60 Hz AC supply. Determine the rmsvalue of currenct in the circuit.
Question
A 60 μF capacitor is connected to a 110 V, 60 Hz AC supply. Determine the rmsvalue of currenct in the circuit.
Solution
To determine the rms value of current in the circuit, we can follow these steps:
Step 1: Calculate the angular frequency (ω) of the AC supply using the formula: ω = 2πf where f is the frequency of the AC supply (60 Hz).
ω = 2π * 60 ω ≈ 377 rad/s
Step 2: Calculate the capacitive reactance (Xc) using the formula: Xc = 1 / (2πfC) where C is the capacitance (60 μF).
Xc = 1 / (2π * 60 * 60 * 10^-6) Xc ≈ 44.18 Ω
Step 3: Calculate the rms value of current (Irms) using Ohm's Law: Irms = Vrms / Xc where Vrms is the rms value of voltage in the circuit (110 V).
Irms = 110 / 44.18 Irms ≈ 2.49 A
Therefore, the rms value of current in the circuit is approximately 2.49 A.
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