Question

Find the terminal voltage of a cell having emf \(12\,V\), internal resistance \(1\,\Omega\), and external resistance \(5\,\Omega\).

• A. \(10\,V\)
• B. \(9.25\,V\)
• C. \(8.5\,V\)
• D. \(7.75\,V\)

Hint:

Terminal voltage while delivering current is \[ V=E-Ir. \] If the cell is not supplying current, terminal voltage equals emf.

Answer 1

The Correct Option is A

Concept: When current flows through a cell, the terminal voltage becomes less than the emf due to the voltage drop across the internal resistance. Current in the circuit is \[ I=\frac{E}{R+r} \] and terminal voltage is \[ V=E-Ir. \]

Step 1: Calculate the current flowing in the circuit. Given, \[ E=12\,V \] \[ R=5\,\Omega \] \[ r=1\,\Omega \] Therefore, \[ I=\frac{12}{5+1} \] \[ I=\frac{12}{6} \] \[ I=2\,A \]

Step 2: Calculate the voltage drop across internal resistance. \[ Ir=(2)(1) \] \[ Ir=2\,V \]

Step 3: Find terminal voltage. \[ V=E-Ir \] \[ V=12-2 \] \[ V=10\,V \]

Step 4: Final answer. \[ \boxed{10\,V} \] Hence, \[ \boxed{(A)} \]