Question 13 of 16beginner🔧 ApplyNumerical1 mark

A 60 μ\muF capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.

Correct Answer

The rms value of current in the circuit is 2.49 A.

Exercise: EXERCISES | Q: 7.4 | (Page 24)
For More Understanding

Explanation

This is a purely capacitive circuit problem. The student needs to first calculate the capacitive reactance using the formula X_C = 1/(2πνC), then apply Ohm's law for AC circuits (I = V/X_C) to find the rms current. The context shows similar calculations in Example 7.6 where capacitive reactance is calculated, and the formula I = V/X_C is demonstrated.

Solution Steps

  1. Step 1: Given values — Capacitance C = 60 μF = 60×1060 \times 10⁻⁶ F, Voltage V = 110 V, Frequency ν = 60 Hz

  2. Step 2: Calculate capacitive reactance — X_C = 1/(2πνC) = 1/(2×3.142 \times 3.14 × 60×6060 \times 60 × 10⁻⁶) = 1/(0.0226) = 44.2 Ω

  3. Step 3: Calculate rms current — I = V/X_C = 110/44.2 = 2.49 A

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