What is the rms current through bulb rated 100 W for 220 V ac supply of 50 Hz?

Options

A. 0.1 A
B. 50 A
C. 0.9 A
D. 0.45 A

Explanation

To find the RMS current through a bulb rated at 100 W for a 220 V AC supply, we can use the formula relating power, voltage, and current. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Power (P) = 100 W
- RMS Voltage (V_rms) = 220 V

### Step 2: Use the formula for power in an AC circuit
The power in an AC circuit can be expressed as:
\[ P = V_{rms} \times I_{rms} \times \cos(\phi) \]
Where:
- \( P \) is the power in watts,
- \( V_{rms} \) is the RMS voltage,
- \( I_{rms} \) is the RMS current,
- \( \cos(\phi) \) is the power factor (which is 1 for a purely resistive load like a bulb).

### Step 3: Rearranging the formula to find \( I_{rms} \)
Assuming the bulb is purely resistive, we can simplify the equation to:
\[ I_{rms} = \frac{P}{V_{rms}} \]

### Step 4: Substitute the known values
Now, substitute the values into the equation:
\[ I_{rms} = \frac{100 \, \text{W}}{220 \, \text{V}} \]

### Step 5: Calculate \( I_{rms} \)
\[ I_{rms} = \frac{100}{220} \]
\[ I_{rms} = \frac{10}{22} \]
\[ I_{rms} = \frac{5}{11} \]
\[ I_{rms} \approx 0.4545 \, \text{A} \]

### Step 6: Final answer
Thus, the RMS current through the bulb is approximately:
\[ I_{rms} \approx 0.45 \, \text{A} \]