Question

Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length l₁ is 40 cm. Now an unknown resistance x is connected in series with P and new balancing length is found to be 80 cm measured from the same end. Then the value of x will be ________ Ω.

Answer 1

Correct Answer: 20

To solve the problem, we apply the principle of the meter bridge, which is based on the Wheatstone bridge concept. The formula used is:

$P/Q\; =\; l$₁/(100-l₁)

Step 1: Initial Setup

• Given: P = 4 Ω
• Balancing length l₁ = 40 cm
• Thus, Q can be calculated using the formula:

$4/Q\; =\; 40/(100-40)$

Solving for Q:

$Q\; =\; 4\; \times \; (60/40)\; =\; 6\; \Omega$

Step 2: Adding Unknown Resistance x

• The new balancing length is 80 cm.
• The circuit now has resistance $(P\; +\; x)$ in series on one side, so:

$(4\; +\; x)/Q\; =\; 80/(100-80)$

Plug in Q = 6 Ω:

$(4\; +\; x)/6\; =\; 80/20$

Solving for x:

$(4\; +\; x)\; =\; 24$

$x\; =\; 24\; -\; 4\; =\; 20\; \Omega$

Confirmation: The calculated value of x is 20 Ω, which falls within the expected range of 20 to 20. Thus, the solution is verified as correct.