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:

Think of internal resistance as something that always opposes the direction current is trying to flow through the cell. Work out separately what happens to terminal voltage when current leaves the cell during discharge versus when current is forced into the cell during charging, and remember the special case where no current flows at all.

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 \[ {(A)} \]