What will happen when a 40 watt 220 volt lamp and 100 watt-220 volt lamp are connected in series across 40 volt supply?

Options

A. 100 watt lamp will fuse
B. 40 watt lamp will fuse
C. Both lamps will fuse
D. Neither lamp will fuse

Answer

To solve the problem of what happens when a 40 watt 220 volt lamp and a 100 watt 220 volt lamp are connected in series across a 40 volt supply, we will follow these steps:

### Step 1: Calculate the Resistance of Each Lamp
The power (P) of a lamp can be expressed in terms of its voltage (V) and resistance (R) using the formula:
\[ P = \frac{V^2}{R} \]
Rearranging this gives:
\[ R = \frac{V^2}{P} \]

**For the 40W lamp:**
- \( P_1 = 40 \, \text{W} \)
- \( V = 220 \, \text{V} \)

Substituting the values:
\[ R_1 = \frac{220^2}{40} = \frac{48400}{40} = 1210 \, \Omega \]

**For the 100W lamp:**
- \( P_2 = 100 \, \text{W} \)

Substituting the values:
\[ R_2 = \frac{220^2}{100} = \frac{48400}{100} = 484 \, \Omega \]

### Step 2: Calculate the Total Resistance in Series
When resistors are connected in series, the total resistance (R) is the sum of the individual resistances:
\[ R = R_1 + R_2 = 1210 \, \Omega + 484 \, \Omega = 1694 \, \Omega \]

### Step 3: Calculate the Current Through the Circuit
Using Ohm's Law, the current (I) flowing through the circuit can be calculated using the formula:
\[ I = \frac{V}{R} \]

Where \( V = 40 \, \text{V} \) (the supply voltage):
\[ I = \frac{40}{1694} \approx 0.0236 \, \text{A} \]

### Step 4: Calculate the Rated Current for Each Lamp
The rated current for each lamp can be calculated using the formula:
\[ I = \frac{V}{R} \]

**For the 40W lamp:**
Using \( R_1 = 1210 \, \Omega \):
\[ I_1 = \frac{220}{1210} \approx 0.1818 \, \text{A} \]

**For the 100W lamp:**
Using \( R_2 = 484 \, \Omega \):
\[ I_2 = \frac{220}{484} \approx 0.4545 \, \text{A} \]

### Step 5: Compare the Actual Current with Rated Current
- The actual current through both lamps is approximately \( 0.0236 \, \text{A} \).
- The rated current for the 40W lamp is approximately \( 0.1818 \, \text{A} \).
- The rated current for the 100W lamp is approximately \( 0.4545 \, \text{A} \).

Since the actual current (0.0236 A) is less than the rated current for both lamps, neither lamp will fuse.

### Conclusion
Thus, when a 40 watt 220 volt lamp and a 100 watt 220 volt lamp are connected in series across a 40 volt supply, **neither lamp will fuse**.

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