Wheatstone Bridge and Balance Condition
A Wheatstone bridge is a four-resistor network used to compare resistances. It is balanced when no current flows through the galvanometer branch, giving the condition P/Q = R/S.
In one line: Balanced bridge means equal middle potentials, so the galvanometer has nothing to detect.
Concept Practice Coming SoonUnderstand it
- In a Wheatstone bridge, four resistors form two potential-divider arms, and a galvanometer connects the middle points.
- At balance, the two middle points are at the same potential, so the galvanometer shows null deflection and carries no current.
- The balance condition then depends only on the ratio of resistances in the two arms, not on the galvanometer resistance.
- This principle is used in resistance measurement and in the metre bridge.
Example
Formula and rule
Balance condition: P/Q = R/S, where P and Q are resistances in one arm and R and S are corresponding resistances in the other arm, all measured in ohm.
Equivalent form: PS = QR.
This condition applies only at null deflection, when galvanometer current is zero.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
A balanced Wheatstone bridge has P = 10 ohm, Q = 20 ohm, and R = 15 ohm.
- 1Using P/Q = R/S, 10/20 = 15/S.
- 2Therefore S = 30 ohm.
- 3Since the bridge is balanced, the galvanometer current is zero and the unknown resistance is 30 ohm.
Method you can reuse
- 1Label the four arms correctly as P, Q, R, and S.
- 2Confirm that the bridge is balanced or the galvanometer current is zero.
- 3Write P/Q = R/S or PS = QR.
- 4Substitute known resistances with ohm units.
- 5Solve for the unknown.
- 6State that galvanometer current is zero at balance.
Sketch it in your answer
Draw a diamond-shaped or rectangular bridge with resistors P, Q, R, and S in four arms, a galvanometer between the two middle junctions, and a cell across the other pair of junctions. Mark the galvanometer current as zero at balance.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
Why does no current flow through the galvanometer in a balanced Wheatstone bridge?
Think first, then show answerHide answer
Common wrong answer
Using the balance formula when the bridge is not balanced.
Why it loses marks: Current then flows through the galvanometer branch and simple ratio equality does not apply.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
A Wheatstone bridge is a four-resistor network used to compare resistances. It is balanced when no current flows through the galvanometer branch, giving the condition P/Q = R/S.
- 2
Add for 2 marks
Example: If P = 2 ohm, Q = 4 ohm, and R = 3 ohm, the bridge is balanced when 2/4 = 3/S, so S = 6 ohm.
- 3
Add for 3 marks
In a Wheatstone bridge, four resistors form two potential-divider arms, and a galvanometer connects the middle points.
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