An electric lamp is marked 60 W, 240 V. If it operats at 200, V the current through it will be

Options

A. `0.18A`
B. `0.21 A`
C. `0.30A`
D. `0.36A`

Answer

To find the current flowing through the electric lamp when it operates at 200 V, we can follow these steps:

### Step 1: Determine the Resistance of the Lamp
The power (P) and voltage (V) ratings of the lamp are given as follows:
- Power, P = 60 W
- Voltage, V = 240 V

We can use the formula for power:
\[ P = \frac{V^2}{R} \]

Rearranging this formula to find resistance (R):
\[ R = \frac{V^2}{P} \]

### Step 2: Substitute the Known Values
Substituting the values into the equation:
\[ R = \frac{(240)^2}{60} \]

### Step 3: Calculate the Resistance
Calculating the square of the voltage:
\[ (240)^2 = 57600 \]

Now substituting this value into the resistance formula:
\[ R = \frac{57600}{60} \]
\[ R = 960 \, \Omega \]

### Step 4: Use Ohm's Law to Find the Current
Now that we have the resistance, we can find the current (I) when the lamp operates at a voltage of 200 V using Ohm's Law:
\[ V = I \times R \]

Rearranging to find current:
\[ I = \frac{V}{R} \]

### Step 5: Substitute the New Voltage and Resistance
Substituting the values:
\[ I = \frac{200}{960} \]

### Step 6: Calculate the Current
Calculating the current:
\[ I = 0.20833 \, \text{A} \]

### Step 7: Round the Answer
Rounding the answer to two decimal places:
\[ I \approx 0.20 \, \text{A} \]

### Final Answer
The current through the lamp when it operates at 200 V is approximately **0.20 A**.

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