Two bulbs 25W, 220V and 100W, 220V are given. Which has higher resistance?

Options

A. 25 w bulb
B. 100 W bulb
C. both bulbs will have equal resistance
D. resistance of bulbs cannot be compared

Explanation

To determine which of the two bulbs has a higher resistance, we can use the formula for resistance in terms of power and voltage:

\[ R = \frac{V^2}{P} \]

Where:
- \( R \) is the resistance,
- \( V \) is the voltage,
- \( P \) is the power.

### Step 1: Calculate the resistance of the 25W bulb
For the 25W bulb:
- Power \( P_{25} = 25W \)
- Voltage \( V = 220V \)

Using the formula:
\[ R_{25} = \frac{V^2}{P_{25}} = \frac{(220)^2}{25} \]

Calculating \( R_{25} \):
\[ R_{25} = \frac{48400}{25} = 1936 \, \Omega \]

### Step 2: Calculate the resistance of the 100W bulb
For the 100W bulb:
- Power \( P_{100} = 100W \)
- Voltage \( V = 220V \)

Using the formula:
\[ R_{100} = \frac{V^2}{P_{100}} = \frac{(220)^2}{100} \]

Calculating \( R_{100} \):
\[ R_{100} = \frac{48400}{100} = 484 \, \Omega \]

### Step 3: Compare the resistances
Now we compare the two resistances:
- \( R_{25} = 1936 \, \Omega \)
- \( R_{100} = 484 \, \Omega \)

Since \( R_{25} > R_{100} \), we conclude that the 25W bulb has a higher resistance than the 100W bulb.

### Final Answer
The 25W bulb has higher resistance.

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