Question

State Ohm's law. Mention any two factors which affect the resistance of a wire. A bulb of 400 W is connected with an electric source of 200 V. The bulb is used only for five minutes. Find the current flowing in the bulb and the magnitude of heat produced in the bulb.

Hint:

The power, current, and voltage in an electrical circuit are related through the formula \( P = VI \). The heat produced can be found using \( H = I^2 R t \), where \( R \) is the resistance, \( I \) is the current, and \( t \) is the time.

Answer 1

Ohm's Law:
Ohm's law states that the current \( I \) flowing through a conductor is directly proportional to the voltage \( V \) across it and inversely proportional to the resistance \( R \) of the conductor. Mathematically, it is expressed as: \[ V = I R \]
where:

- \( V \) is the potential difference (voltage) across the conductor (in volts),
- \( I \) is the current flowing through the conductor (in amperes),
- \( R \) is the resistance of the conductor (in ohms).

Factors affecting the resistance of a wire:
The resistance \( R \) of a wire depends on the following factors:
1.
Material of the conductor:
Different materials have different resistances. For example, copper and aluminum have low resistance, while rubber and glass have high resistance. 2.
Length of the conductor:
The resistance of a conductor is directly proportional to its length. The longer the conductor, the higher the resistance. \[ R \propto l \] Where \( l \) is the length of the conductor.
Given Information:
- Power of the bulb \( P = 400 \, \text{W} \)
- Voltage across the bulb \( V = 200 \, \text{V} \)
- Time of use \( t = 5 \, \text{minutes} = 300 \, \text{seconds} \)
Step 1: Finding the current flowing in the bulb:
Using the formula for power: \[ P = V \times I \] We can rearrange this to solve for \( I \) (current): \[ I = \frac{P}{V} \] Substituting the given values: \[ I = \frac{400}{200} = 2 \, \text{A} \] So, the current flowing through the bulb is \( 2 \, \text{A} \).
Step 2: Finding the heat produced in the bulb:
The heat produced in a conductor is given by the formula: \[ H = I^2 R t \] First, we need to find the resistance \( R \) of the bulb. Using Ohm's law: \[ R = \frac{V}{I} \] Substituting the known values: \[ R = \frac{200}{2} = 100 \, \Omega \] Now, calculating the heat produced: \[ H = (2)^2 \times 100 \times 300 = 4 \times 100 \times 300 = 120000 \, \text{J} \]
Conclusion:
- The current flowing in the bulb is \( 2 \, \text{A} \).
- The heat produced in the bulb is \( 120000 \, \text{J} \).