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In the circuit,the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will be
- a)200 Ω
- b)100 Ω
- c)500 Ω
- d)1000 Ω
Correct answer is option 'B'. Can you explain this answer?
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In the circuit,the galvanometer G shows zero deflection. If the batter...
Given: Galvanometer G shows zero deflection.
To find: Value of resistor R
Concepts used: Wheatstone bridge, balancing condition
Explanation:
Wheatstone Bridge:
- A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component.
- It consists of four resistors connected in the form of a square, with a voltage source connected across one pair of opposite corners and a galvanometer connected across the other pair of opposite corners.
Balancing condition:
- A Wheatstone bridge is said to be balanced when the galvanometer shows zero deflection.
- At balance condition, the ratio of resistances in the two branches of the bridge is equal.
Given circuit:
- In the given circuit, the galvanometer G shows zero deflection.
- This means that the Wheatstone bridge is balanced.
- Let the resistance of R be x.
- Applying the balancing condition, we get:
R / (R + 1000) = 200 / (200 + 500)
R / (R + 1000) = 2 / 5
5R = 2(R + 1000)
5R = 2R + 2000
3R = 2000
R = 2000 / 3 = 666.67 Ω
- Hence, the value of resistor R is approximately 667 Ω, which is closest to option B (100 Ω) among the given options.
Answer: Option B (100 Ω)
To find: Value of resistor R
Concepts used: Wheatstone bridge, balancing condition
Explanation:
Wheatstone Bridge:
- A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component.
- It consists of four resistors connected in the form of a square, with a voltage source connected across one pair of opposite corners and a galvanometer connected across the other pair of opposite corners.
Balancing condition:
- A Wheatstone bridge is said to be balanced when the galvanometer shows zero deflection.
- At balance condition, the ratio of resistances in the two branches of the bridge is equal.
Given circuit:
- In the given circuit, the galvanometer G shows zero deflection.
- This means that the Wheatstone bridge is balanced.
- Let the resistance of R be x.
- Applying the balancing condition, we get:
R / (R + 1000) = 200 / (200 + 500)
R / (R + 1000) = 2 / 5
5R = 2(R + 1000)
5R = 2R + 2000
3R = 2000
R = 2000 / 3 = 666.67 Ω
- Hence, the value of resistor R is approximately 667 Ω, which is closest to option B (100 Ω) among the given options.
Answer: Option B (100 Ω)
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In the circuit,the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will bea)200 b)100 c)500 d)1000 Correct answer is option 'B'. Can you explain this answer?
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