Two bulbs are fitted in a room in the domestic electric installation. If one of them glows brighter than the other, then

Options

A. the brighter bulb has smaller resistance
B. the brighter bulb has larger resistance
C. both the bulbs have the same resistance
D. nothing can be said about the resistance unless other factors are known.

Answer

To solve the problem of why one bulb glows brighter than the other in a domestic electric installation, we can follow these steps:

### Step 1: Understand the Setup
In a domestic electric installation, the bulbs are typically connected in parallel. This means that each bulb receives the same voltage from the power supply.

**Hint:** Remember that in a parallel circuit, the voltage across each component is the same.

### Step 2: Analyze the Brightness of Bulbs
The brightness of a bulb is related to the amount of power it consumes, which is determined by the heat generated in the filament. The power (P) consumed by a bulb can be expressed as:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage across the bulb and \( R \) is the resistance of the bulb.

**Hint:** Power is directly proportional to the voltage squared and inversely proportional to the resistance.

### Step 3: Compare the Bulbs
Since both bulbs are connected in parallel, they have the same voltage \( V \). If one bulb is glowing brighter than the other, it must be consuming more power. Therefore, we can conclude:
\[ P_1 > P_2 \]
where \( P_1 \) is the power of the brighter bulb and \( P_2 \) is the power of the dimmer bulb.

**Hint:** If one bulb is brighter, it must be using more power.

### Step 4: Relate Power to Resistance
From the power formula, if the voltage is constant, the power consumed by each bulb is inversely related to its resistance. Thus, if one bulb is consuming more power (brighter), it must have a smaller resistance:
\[ R_1 < R_2 \]
where \( R_1 \) is the resistance of the brighter bulb and \( R_2 \) is the resistance of the dimmer bulb.

**Hint:** Lower resistance leads to higher power consumption when voltage is constant.

### Step 5: Conclusion
Therefore, we conclude that the brighter bulb has a smaller resistance compared to the dimmer bulb.

**Final Answer:** The brighter bulb has smaller resistance.