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

Options

A. `25 W` bulb
B. `100 W` bulb
C. Both bulb will have equal resistance
D. Resistance of bulbs cannot be compared

Answer

To determine which bulb has a higher resistance, we can use the formula relating power (P), voltage (V), and resistance (R):

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

From this, we can rearrange the formula to find resistance:

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

Now, let's calculate the resistance for each bulb.

### Step 1: Calculate the resistance of the 25 W bulb
- Given:
- Power (P) = 25 W
- Voltage (V) = 220 V

Using the formula:

\[ R_{25W} = \frac{V^2}{P} = \frac{220^2}{25} \]

Calculating \( 220^2 \):

\[ 220^2 = 48400 \]

Now substituting:

\[ R_{25W} = \frac{48400}{25} = 1936 \, \Omega \]

### Step 2: Calculate the resistance of the 100 W bulb
- Given:
- Power (P) = 100 W
- Voltage (V) = 220 V

Using the same formula:

\[ R_{100W} = \frac{V^2}{P} = \frac{220^2}{100} \]

Using \( 220^2 = 48400 \):

\[ R_{100W} = \frac{48400}{100} = 484 \, \Omega \]

### Step 3: Compare the resistances
Now we have:

- Resistance of the 25 W bulb: \( R_{25W} = 1936 \, \Omega \)
- Resistance of the 100 W bulb: \( R_{100W} = 484 \, \Omega \)

Since \( 1936 \, \Omega > 484 \, \Omega \), we conclude that the 25 W bulb has a higher resistance.

### Final Answer:
The 25 W bulb has a higher resistance than the 100 W bulb.

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