A `30 mu F` capacitor is connected to a 150 V, 60 Hz ac supply. The rms value of current in the circuit is

Options

A. 17 A
B. `1.7 A`
C. `1.7 mA`
D. `2.7 A`

Explanation

To solve the problem, we need to find the RMS value of the current flowing through a capacitor connected to an AC supply. Here are the steps to arrive at the solution:

### Step 1: Identify the given values
- Capacitance, \( C = 30 \, \mu F = 30 \times 10^{-6} \, F \)
- Voltage, \( V = 150 \, V \)
- Frequency, \( f = 60 \, Hz \)

### Step 2: Calculate the capacitive reactance \( X_c \)
The capacitive reactance \( X_c \) is given by the formula:
\[ X_c = \frac{1}{2 \pi f C} \]
Substituting the values:
\[ X_c = \frac{1}{2 \pi (60) (30 \times 10^{-6})} \]

### Step 3: Perform the calculation for \( X_c \)
Calculating \( X_c \):
\[ X_c = \frac{1}{2 \pi (60) (30 \times 10^{-6})} \approx 88.46 \, \Omega \]

### Step 4: Calculate the RMS value of the current \( I_{RMS} \)
The RMS value of the current is calculated using the formula:
\[ I_{RMS} = \frac{V_{RMS}}{X_c} \]
Substituting the values:
\[ I_{RMS} = \frac{150}{88.46} \]

### Step 5: Perform the calculation for \( I_{RMS} \)
Calculating \( I_{RMS} \):
\[ I_{RMS} \approx 1.695 \, A \]

### Step 6: Round off the answer
Rounding off \( 1.695 \, A \) gives:
\[ I_{RMS} \approx 1.7 \, A \]

### Final Answer
The RMS value of the current in the circuit is approximately \( 1.7 \, A \).

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