A steel wire has a resistance twice that of an aluminium wire. Both of them are connected with a constant voltage supply. More heat will be dissipated in

Options

A. steel wire when both are connected in series
B. steel wire when both are connected in parallel
C. aluminium wire when both are connected in series
D. aluminium wire when both are connected in parallel.

Answer

To solve the problem, we need to analyze the heat dissipation in both the steel and aluminum wires under two different configurations: series and parallel.

### Step-by-Step Solution:

1. **Understanding Resistance**:
- Let the resistance of the aluminum wire be \( R \).
- Then, the resistance of the steel wire is \( 2R \) (as given in the problem).

2. **Heat Dissipation in Series Connection**:
- When connected in series, the same current \( I \) flows through both wires.
- The heat dissipated \( H \) in a resistor is given by the formula:
\[ H = I^2 R t \]
- For the aluminum wire:
\[ H_{Al} = I^2 R t \]
- For the steel wire:
\[ H_{Steel} = I^2 (2R) t = 2 I^2 R t \]
- Since \( H_{Steel} = 2 H_{Al} \), more heat will be dissipated in the steel wire when connected in series.

3. **Heat Dissipation in Parallel Connection**:
- When connected in parallel, the voltage \( V \) across both wires is the same.
- Using Ohm's law, the current through each wire can be expressed as:
\[ I_{Al} = \frac{V}{R} \quad \text{and} \quad I_{Steel} = \frac{V}{2R} \]
- The current through the aluminum wire is twice that of the steel wire:
\[ I_{Steel} = \frac{1}{2} I_{Al} \]
- The heat dissipated in the aluminum wire:
\[ H_{Al} = V I_{Al} t = V \left(\frac{V}{R}\right) t = \frac{V^2}{R} t \]
- The heat dissipated in the steel wire:
\[ H_{Steel} = V I_{Steel} t = V \left(\frac{V}{2R}\right) t = \frac{V^2}{2R} t \]
- Since \( H_{Al} = 2 H_{Steel} \), more heat will be dissipated in the aluminum wire when connected in parallel.

4. **Conclusion**:
- In series connection, more heat is dissipated in the steel wire.
- In parallel connection, more heat is dissipated in the aluminum wire.

### Final Answer:
- More heat will be dissipated in the steel wire when both are connected in series, and more heat will be dissipated in the aluminum wire when both are connected in parallel.