The Question is from neet-physics current-electricity , and it was created by the author ABDUL JILANI BASHA

Question

A metre bridge is balanced with a known resistance of 20 $\Omega$ in the right gap and an unknown resistance in the left gap. If the balance point is at 60 cm from the left end, what is the value of the unknown resistance?

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
 **Primary Concept**: Meter Bridge Principle (Wheatstone Bridge)
 **Related Topics**: Resistance, balancing length, Wheatstone bridge applications
 **Prerequisites**: Understanding of Wheatstone bridge, Ohm's law.
## SOLUTION PATHWAY
**Given Information**:
  Known resistance ($R_2$) = 20 $\Omega$
  Balancing length ($l_1$) = 60 cm
  Total length of the meter bridge ($l$) = 100 cm
  Unknown resistance ($R_1$) = ?
**Method & Steps**:
 1. Apply the principle of the meter bridge (Wheatstone bridge).
  Reasoning: At the balance point, the ratio of resistances is equal to the ratio of lengths.
  Formula/Rule: $\frac{R_1}{R_2} = \frac{l_1}{l_2}$ where $l_2 = l - l_1$
 2. Substitute the given values into the formula.
  Working: $\frac{R_1}{20} = \frac{60}{100 - 60} = \frac{60}{40} = \frac{3}{2}$
 3. Solve for the unknown resistance ($R_1$).
  Result: $R_1 = 20 	imes \frac{3}{2} = 30 \Omega$
  Verification: Substitute the calculated value back into the formula to verify the balance condition.
 ## OPTION ANALYSIS
A ✓: 30 $\Omega$ is the correct answer obtained by applying the meter bridge principle and solving the equation.
B :x: 15 $\Omega$ is incorrect; it results from an incorrect calculation or misunderstanding of the principle.
C :x: 25 $\Omega$ is incorrect; it results from an incorrect calculation or misunderstanding of the principle.
D :x: 40 $\Omega$ is incorrect; it results from an incorrect calculation or misunderstanding of the principle.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Incorrectly calculating the ratio of lengths: Ensure to use the correct lengths ($l_1$ and $l_2$) in the ratio.
  2.Unit error: Always maintain consistent units (cm for lengths and $\Omega$ for resistance).
 **Quick Tips**:
  1.Remember the simple formula $\frac{R_1}{R_2} = \frac{l_1}{l_2}$ and use it directly after finding the lengths.
  2.Always double-check your calculation to avoid arithmetic errors.

ABDUL JILANI BASHA · Answer

The correct Option is "30 $\Omega$"

ABDUL JILANI BASHA · Answer

15 $\Omega$

ABDUL JILANI BASHA · Answer

25 $\Omega$

ABDUL JILANI BASHA · Answer

40 $\Omega$

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