To determine which bulb will fuse when the two bulbs are connected in series to a 440 V supply, we can follow these steps:
### Step 1: Understand the Bulb Ratings
We have two bulbs:
- Bulb 1: 25 W, 220 V
- Bulb 2: 100 W, 220 V
### Step 2: Calculate the Current Ratings of Each Bulb
The current through each bulb can be calculated using the formula:
\[
I = \frac{P}{V}
\]
where \( P \) is the power rating and \( V \) is the voltage rating.
**For Bulb 1:**
\[
I_1 = \frac{25 \, \text{W}}{220 \, \text{V}} = 0.1136 \, \text{A}
\]
**For Bulb 2:**
\[
I_2 = \frac{100 \, \text{W}}{220 \, \text{V}} = 0.4545 \, \text{A}
\]
### Step 3: Calculate the Resistance of Each Bulb
The resistance of each bulb can be calculated using the formula:
\[
R = \frac{V^2}{P}
\]
**For Bulb 1:**
\[
R_1 = \frac{220^2}{25} = 1936 \, \Omega
\]
**For Bulb 2:**
\[
R_2 = \frac{220^2}{100} = 484 \, \Omega
\]
### Step 4: Calculate the Total Resistance in Series
Since the bulbs are connected in series, the total resistance \( R_{\text{eq}} \) is:
\[
R_{\text{eq}} = R_1 + R_2 = 1936 \, \Omega + 484 \, \Omega = 2420 \, \Omega
\]
### Step 5: Calculate the Total Current Through the Circuit
Using Ohm's law, the total current \( I \) when a 440 V supply is connected can be calculated as:
\[
I = \frac{V}{R_{\text{eq}}} = \frac{440 \, \text{V}}{2420 \, \Omega} = 0.1818 \, \text{A}
\]
### Step 6: Compare the Current Ratings
Now we compare the calculated current \( I \) with the rated currents of the bulbs:
- \( I_1 = 0.1136 \, \text{A} \)
- \( I_2 = 0.4545 \, \text{A} \)
- \( I = 0.1818 \, \text{A} \)
### Step 7: Determine Which Bulb Will Fuse
- For Bulb 1: The rated current \( I_1 \) (0.1136 A) is less than the current \( I \) (0.1818 A), so Bulb 1 can handle this current.
- For Bulb 2: The rated current \( I_2 \) (0.4545 A) is greater than the current \( I \) (0.1818 A), meaning Bulb 2 is rated for a higher current than what is flowing through it.
Since Bulb 1 has a lower rated current than the current flowing through it, it will fuse.
### Conclusion
The bulb that will fuse is the **25 W bulb**.
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