Question

For a cell or a battery, the emf is (A) equal to the potential difference between its terminals when terminals are not connected externally (B) less than the potential difference between its terminals when the cell/battery is being discharged (C) always greater than the potential difference between its terminals (D) less than the potential difference between its terminals when the cell/battery is being charged Choose the correct answer from the options given below:

• A. (A) and (D) only
• B. (A) and (C) only
• C. (C) only
• D. (A), (B) and (C) only

Hint:

Remember: During discharge: \[ V=E-Ir \] During charging: \[ V=E+Ir \] Open circuit: \[ V=E \] These three relations solve almost all emf and internal resistance MCQs.

Answer 1

The Correct Option is A

Concept: For a cell of emf \(E\), terminal potential difference \(V\), current \(I\), and internal resistance \(r\): During discharging, \[ V=E-Ir \] During charging, \[ V=E+Ir \]

Step 1:Check statement (A). When the cell is not connected externally, \[ I=0 \] Therefore, \[ V=E \] Hence, \[ {\text{Statement (A) is true.}} \]

Step 2: Check statement (B). During discharging, \[ V=E-Ir \] which implies \[ V<E \] or \[ E>V \] Thus emf is greater than the terminal potential difference. Hence, \[ {\text{Statement (B) is false.}} \]

Step 3: Check statement (C). When discharging, \[ E>V \] but when the cell is open, \[ E=V \] Therefore emf is not always greater than terminal voltage. Hence, \[ {\text{Statement (C) is false.}} \]

Step 4: Check statement (D). During charging, \[ V=E+Ir \] Therefore, \[ V>E \] or \[ E<V \] Hence emf is less than the terminal potential difference. \[ {\text{Statement (D) is true.}} \]

Step 5: State the answer. \[ { \text{Statements (A) and (D) are correct.} } \] Hence, the correct option is \[ {(A)} \]