Question
Download Solution PDFTwo resistances 1Ω and 4Ω are connected in the left and right gaps of a Wheatstone's meter bridge. The balancing length 'l' is noted. Now the resistances are interchanged in the two gaps. The new balancing length 'L' is noted Then
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Meter Bridge:
- A meter bridge also called a slide wire bridge is an instrument that works on the principle of a Wheatstone bridge.
- A meter bridge is used in finding the unknown resistance of a conductor as that of in a Wheatstone bridge.
- In a meter bridge, a wire having a length of a uniform cross-section of about 1m is used.
- One known resistance and an unknown resistance are connected as shown in the figure.
- The one part of the galvanometer is connected in between the known and unknown resistances, whereas the other part of the wire is used to find the null point where the galvanometer is not showing any deflection.
- At this point, the bridge is said to be balanced.
- In the case of a meter bridge, the resistance wire AC is 100 cm long. Varying the position of tapping point B, the bridge is balanced.
- If in the balanced position of bridge AB = l, BC (100 – l) so that
\(\frac{Q}{P} = \frac{{\left( {100 - l} \right)}}{l}\)
Also, \(\frac{P}{Q} = \frac{R}{S} \Rightarrow S = \frac{{\left( {100 - l} \right)}}{l}R\)
Calculation:
Given: P = R1 = 1Ω, Q = R2 = 4Ω
\(\frac{P}{Q} = \frac{R}{S} \Rightarrow \frac{l}{L}= \frac{1}{4}\)
So, \(\frac{l}{L} = \frac{1}{4}\)
Last updated on May 6, 2025
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