A `60 mu F` capacitor is connected to a 110 V, 60 Hz a.c. supply Determine the r.m.s value of current in the circuit.

Options

A. `1.49 A`
B. `14.9 A`
C. `2.49 A`
D. `24.9 A`

Answer

To determine the r.m.s value of current in the circuit with a capacitor connected to an AC supply, we can follow these steps:

### Step 1: Identify the given values
- Capacitance (C) = 60 µF = 60 × 10^(-6) F
- Voltage (V_rms) = 110 V
- Frequency (f) = 60 Hz

### Step 2: Calculate the capacitive reactance (X_c)
The formula for capacitive reactance is given by:
\[ X_c = \frac{1}{2 \pi f C} \]

Substituting the values:
\[ X_c = \frac{1}{2 \pi (60) (60 \times 10^{-6})} \]

### Step 3: Perform the calculations
1. Calculate \( 2 \pi \times 60 \):
\[ 2 \pi \times 60 \approx 376.99 \]

2. Now calculate \( X_c \):
\[ X_c = \frac{1}{376.99 \times 60 \times 10^{-6}} \]
\[ X_c \approx \frac{1}{0.000022619} \]
\[ X_c \approx 44.23 \, \Omega \]

### Step 4: Calculate the r.m.s value of current (I_rms)
The formula for the r.m.s value of current in a capacitive circuit is:
\[ I_{rms} = \frac{V_{rms}}{X_c} \]

Substituting the values:
\[ I_{rms} = \frac{110}{44.23} \]

### Step 5: Perform the final calculation
1. Calculate \( I_{rms} \):
\[ I_{rms} \approx 2.48 \, A \]

### Final Answer
The r.m.s value of current in the circuit is approximately **2.48 A**.

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