Question

In a potentiometer circuit when two cells of e.m.f. \(1.5\) volt and \(1.2\) volt are connected to assist each other, balancing length is \(270\) cm. What will be the balancing length in cm when these two cells are connected in opposition?

• A. \(90\)
• B. \(81\)
• C. \(60\)
• D. \(30\)

Hint:

Balancing length is proportional to the net e.m.f.

Answer 1

The Correct Option is D

Step 1: Principle:
In a potentiometer the balancing length is proportional to the e.m.f.: \(E\propto l\).

Step 2: Cells Assisting:
Net e.m.f. \(=1.5+1.2=2.7\) V and \(l=270\) cm. So the potential gradient is \(\dfrac{2.7}{270}=0.01\) V/cm.

Step 3: Cells in Opposition:
Net e.m.f. \(=1.5-1.2=0.3\) V. Balancing length \(=\dfrac{0.3}{0.01}=30\) cm.

Step 4: Check the Other Options:
90 cm, 81 cm and 60 cm correspond to e.m.f.s of 0.9 V, 0.81 V and 0.6 V, none of which equals 0.3 V.

Final Answer:
The balancing length is 30 cm, option (D). \[ \boxed{\text{(D) } 30\ \text{cm}} \]