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In a Wheatstone's bridge, all the four arms have equal resistance R. If resistance of the galvanometer arm is also R, then equivalent resistance of the combination is
- a)R
- b)2R
- c)R/2
- d)R/4
Correct answer is option 'A'. Can you explain this answer?
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In a Wheatstones bridge, all the four arms have equal resistance R. If...
**Explanation:**
**Wheatstone's Bridge:**
- A Wheatstone bridge is a circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit.
- It consists of four resistors forming a closed loop with a galvanometer connected between two junctions.
**Given Information:**
- All four arms of the Wheatstone bridge have equal resistance R.
- Resistance of the galvanometer arm is also R.
**Calculating Equivalent Resistance:**
- Let's denote the four arms of the bridge as R1, R2, R3, and R4.
- Since all arms have equal resistance R, R1 = R2 = R3 = R4 = R.
- The resistance of the galvanometer arm is also R.
- The galvanometer arm is in parallel with R4, so the equivalent resistance of R4 and the galvanometer arm is (R x R) / (R + R) = R/2.
- Now, the two parallel combinations R3 and R4 + galvanometer arm R are in series, so their equivalent resistance is R + R/2 = 3R/2.
- The equivalent resistance of R1 and R2 is R + R = 2R.
- The two series combinations R1 and R2, and R3 + R4 + galvanometer arm are in parallel, so the total equivalent resistance is (2R x 3R/2) / (2R + 3R/2) = R.
Therefore, the equivalent resistance of the combination is **R (option A)**.
**Wheatstone's Bridge:**
- A Wheatstone bridge is a circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit.
- It consists of four resistors forming a closed loop with a galvanometer connected between two junctions.
**Given Information:**
- All four arms of the Wheatstone bridge have equal resistance R.
- Resistance of the galvanometer arm is also R.
**Calculating Equivalent Resistance:**
- Let's denote the four arms of the bridge as R1, R2, R3, and R4.
- Since all arms have equal resistance R, R1 = R2 = R3 = R4 = R.
- The resistance of the galvanometer arm is also R.
- The galvanometer arm is in parallel with R4, so the equivalent resistance of R4 and the galvanometer arm is (R x R) / (R + R) = R/2.
- Now, the two parallel combinations R3 and R4 + galvanometer arm R are in series, so their equivalent resistance is R + R/2 = 3R/2.
- The equivalent resistance of R1 and R2 is R + R = 2R.
- The two series combinations R1 and R2, and R3 + R4 + galvanometer arm are in parallel, so the total equivalent resistance is (2R x 3R/2) / (2R + 3R/2) = R.
Therefore, the equivalent resistance of the combination is **R (option A)**.
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In a Wheatstones bridge, all the four arms have equal resistance R. If resistance of the galvanometer arm is also R, then equivalent resistance of the combination isa)Rb)2Rc)R/2d)R/4Correct answer is option 'A'. Can you explain this answer?
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