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A meter bridge is used to determine the resistance of an unknown wire by measuring the balance point length l. If the wire is replaced by another wire of same material but with double the length and half the thickness, the balancing point is expected to be
- a)1 / 8l
- b)1 / 4l
- c)8l
- d)16l
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A meter bridge is used to determine the resistance of an unknown wire...
In a meter bridge the ratio of two resistances is
Where l and l′ are balancing lengths.
Resistance 
In material remains same ρ = ρ′
Given, l′ = 2l
r′ = r / 2
∴ 
R′ = 8R
Therefore, the new balancing point is expected to be 8l.
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Community Answer
A meter bridge is used to determine the resistance of an unknown wire...
The meter bridge is a device used to measure the resistance of an unknown wire by finding the balance point. The balance point is the position on the meter bridge where there is no current flowing through the galvanometer, indicating that the resistance on both sides of the bridge is equal.
When the wire is replaced by another wire of the same material but with double the length and half the thickness, the balancing point is expected to change. Let's understand why this happens:
1. Resistance of a wire:
- The resistance of a wire depends on its length, cross-sectional area, and resistivity of the material.
- The resistance of a wire is directly proportional to its length and resistivity, and inversely proportional to its cross-sectional area.
2. Effect of doubling the length:
- When the length of the wire is doubled, its resistance also doubles.
- This happens because the longer wire offers more opposition to the flow of current.
3. Effect of halving the thickness:
- When the thickness of the wire is halved, its resistance becomes four times.
- This happens because the cross-sectional area is reduced by half, which increases the resistance.
4. Balancing point on the meter bridge:
- The balancing point on the meter bridge depends on the ratio of the resistances on both sides of the bridge.
- If the resistances on both sides are equal, the bridge is balanced, and no current flows through the galvanometer.
- The balancing point is determined by adjusting the position of the jockey on the wire.
5. Changes in balancing point:
- When the wire is replaced by another wire with double the length and half the thickness, the resistance of the wire changes.
- Doubling the length of the wire doubles its resistance, while halving the thickness increases its resistance four times.
- As a result, the overall resistance of the wire increases.
- To balance the bridge, the jockey needs to be moved towards the unknown wire, indicating that the balancing point has shifted towards the unknown wire.
Therefore, the balancing point is expected to be 8 times the original length (8l) when the wire is replaced by another wire with double the length and half the thickness. So, option 'C' is the correct answer.
When the wire is replaced by another wire of the same material but with double the length and half the thickness, the balancing point is expected to change. Let's understand why this happens:
1. Resistance of a wire:
- The resistance of a wire depends on its length, cross-sectional area, and resistivity of the material.
- The resistance of a wire is directly proportional to its length and resistivity, and inversely proportional to its cross-sectional area.
2. Effect of doubling the length:
- When the length of the wire is doubled, its resistance also doubles.
- This happens because the longer wire offers more opposition to the flow of current.
3. Effect of halving the thickness:
- When the thickness of the wire is halved, its resistance becomes four times.
- This happens because the cross-sectional area is reduced by half, which increases the resistance.
4. Balancing point on the meter bridge:
- The balancing point on the meter bridge depends on the ratio of the resistances on both sides of the bridge.
- If the resistances on both sides are equal, the bridge is balanced, and no current flows through the galvanometer.
- The balancing point is determined by adjusting the position of the jockey on the wire.
5. Changes in balancing point:
- When the wire is replaced by another wire with double the length and half the thickness, the resistance of the wire changes.
- Doubling the length of the wire doubles its resistance, while halving the thickness increases its resistance four times.
- As a result, the overall resistance of the wire increases.
- To balance the bridge, the jockey needs to be moved towards the unknown wire, indicating that the balancing point has shifted towards the unknown wire.
Therefore, the balancing point is expected to be 8 times the original length (8l) when the wire is replaced by another wire with double the length and half the thickness. So, option 'C' is the correct answer.
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A meter bridge is used to determine the resistance of an unknown wire by measuring the balance point length l. If the wire is replaced by another wire of same material but with double the length and half the thickness, the balancing point is expected to bea)1 / 8lb)1 / 4lc)8ld)16lCorrect answer is option 'C'. Can you explain this answer?
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