Meter Bridge

A meter bridge is a practical Wheatstone bridge in which a uniform wire of length 100 cm replaces two arms, so the ratio of resistances equals the ratio of the corresponding lengths. With the unknown (X) in the left gap and known (R) in the right gap, the balance condition reads (\frac{X}{R} = \frac{l}{100 - l}), where (l) is the balancing length from the left. Here (l = 40) cm and (R = 9;\Omega), so (X = 9 \times \frac{40}{60} = 9 \times \frac{2}{3} = 6;\Omega). The value 13.5 (\Omega) is wrong because it inverts the length ratio. The value 4 (\Omega) mistakenly squares part of the ratio. The value 9 (\Omega) wrongly assumes balance occurs only when both arms are equal. This uses the NCERT meter-bridge formula derived from the Wheatstone balance condition. A sanity check confirms it: because the balancing length on the unknown side (40 cm) is shorter than the other side (60 cm), the unknown must be smaller than 9 (\Omega), consistent with 6 (\Omega). In careful experimental practice the most reliable readings are taken when the balance point lies near the middle of the wire, because the percentage error in the length measurement, and hence in the deduced resistance, is minimised there compared with balance points crowded close to either end of the bridge wire.