Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A potentiometer wire of length 120 cm and resistance 8 ohms is connected to a battery of emf E and an external resistor of resistance 12 ohms in series. The balance point is obtained

A potentiometer wire of length 120 cm and resistance 8 ohms is connected
to a battery of emf E and an external resistor of resistance 12 ohms in
series. The balance point is obtained at a length of 90 cm from the positive
end of the wire. Calculate the internal resistance r of the cell.

Option: 1

0.6 ohms


Option: 2

1.2 ohms


Option: 3

16 ohms


Option: 4

2.4 ohms


Answers (1)

best_answer

Step 1: In a potentiometer setup, the potential difference across the length l of the wire is given by:

V=\frac{E l}{L}

Given: Length of the wire (L) = 120 cm Length of the balance point (l) = 90 cm Resistance of the potentiometer wire (R) = 8 ohms Resistance of the external resistor (R_{\text {ext }}) = 12 ohms
Step 2: Calculate the total resistance in the circuit.
Total resistance = R + R_{\text {ext }} = 8 ohms + 12 ohms = 20 ohms
Step 3: Calculate the potential difference (V ) across the potentiometer wire using the potential difference formula.

V=\frac{E \cdot l}{L}

E=\frac{V \cdot L}{l}=\frac{V \cdot 120}{90}

Step 4: Calculate the current (I) in the circuit using Ohm’s law.

I=\frac{V}{R_{\text {ext }}}=\frac{V}{12}

Step 5: Apply the formula for emf (E) in terms of internal resistance (r) and current (I).

E = Ir + V

\frac{V \cdot 120}{90}=\frac{V}{12} \cdot r+V

Step 6: Solve for the internal resistance (r).

\frac{V \cdot 120}{90}-V=\frac{V}{12} \cdot r

\frac{4}{3} V=\frac{V}{12} \cdot r

r=\frac{4}{3} \cdot 12=16 \mathrm{ohms}

So, the internal resistance (r) of the cell is 16 ohms. Therefore, the correct answer C.

Posted by

Anam Khan

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main Marks vs Percentile 2025: How many marks do you need to score 95+ percentile?
anam-khan

JEE Main 2025 session 1 official answer key out; challenge by February 6; how to calculate NTA score?
anam-khan

JEE Main 2025: NIT Raipur's CSE cut-offs drop; closing ranks in popular branches

Latest Question