Two electric bulbs one, if 200 V-40 W and other 200 V-100 W are connected in series to a 200 V line, then the potential drop across

Options

A. the two bulbs is the same
B. Both the bulbs is 200 V
C. 40 W bulb is greater than the potential drop across 100 W bulb
D. 100 W bulb is greater than the potential drop across 40 W bulb

Answer

To solve the problem of finding the potential drop across two electric bulbs connected in series, we will follow these steps:

### Step 1: Determine the Resistance of Each Bulb
We know the power (P) and voltage (V) for each bulb. The resistance (R) can be calculated using the formula:
\[ R = \frac{V^2}{P} \]

For the 40 W bulb:
\[ R_1 = \frac{(200 \, \text{V})^2}{40 \, \text{W}} = \frac{40000}{40} = 1000 \, \Omega \]

For the 100 W bulb:
\[ R_2 = \frac{(200 \, \text{V})^2}{100 \, \text{W}} = \frac{40000}{100} = 400 \, \Omega \]

### Step 2: Calculate the Total Resistance in the Circuit
Since the bulbs are connected in series, the total resistance (R_total) is the sum of the individual resistances:
\[ R_{\text{total}} = R_1 + R_2 = 1000 \, \Omega + 400 \, \Omega = 1400 \, \Omega \]

### Step 3: Calculate the Current Flowing Through the Circuit
Using Ohm's Law, the current (I) in the circuit can be calculated using the total voltage (V_total) and the total resistance (R_total):
\[ I = \frac{V_{\text{total}}}{R_{\text{total}}} = \frac{200 \, \text{V}}{1400 \, \Omega} = \frac{1}{7} \, \text{A} \]

### Step 4: Calculate the Voltage Drop Across Each Bulb
Now we can find the voltage drop across each bulb using Ohm's Law (V = IR).

For the 40 W bulb:
\[ V_1 = I \times R_1 = \left(\frac{1}{7} \, \text{A}\right) \times (1000 \, \Omega) = \frac{1000}{7} \, \text{V} \approx 142.86 \, \text{V} \]

For the 100 W bulb:
\[ V_2 = I \times R_2 = \left(\frac{1}{7} \, \text{A}\right) \times (400 \, \Omega) = \frac{400}{7} \, \text{V} \approx 57.14 \, \text{V} \]

### Step 5: Conclusion
The potential drop across the 40 W bulb is approximately 142.86 V, and the potential drop across the 100 W bulb is approximately 57.14 V. Therefore, the potential difference across the 40 W bulb is greater than that across the 100 W bulb.

### Final Answer
The potential drop across the 40 W bulb is greater than that across the 100 W bulb.

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