Question

A resistance R is connected across a cell with a switch and a rheostat in series. A voltmeter is connected parallel across the cell. Current in the circuit is increased using the rheostat.
(a) How will the voltmeter reading change? (increase / decrease / remain the same)
(b) Justify your answer stated in (a) above.

Hint:

Think of terminal voltage as the "usable voltage" from a cell. The more current you draw, the more voltage is "lost" inside the cell itself, so the less is available to the external circuit.

Answer 1

Step 1: Understanding the Concept:
A voltmeter connected across a cell measures the terminal voltage (\( V \)), which is the potential difference across the cell's terminals when current is flowing.
Step 2: Key Formula or Approach:
The relationship between Terminal Voltage (\( V \)), EMF (\( E \)), Current (\( I \)), and internal resistance (\( r \)) is:
\[ V = E - I \cdot r \]
Step 3: Detailed Explanation:
When the rheostat is adjusted to increase the current (\( I \)) in the circuit:
1. The EMF (\( E \)) and internal resistance (\( r \)) of the cell remain constant.
2. The term \( I \cdot r \), which represents the "lost voltage" or potential drop inside the cell, increases as \( I \) increases.
3. Since \( V = E - (Ir) \), an increase in the subtracted term results in a decrease in the terminal voltage \( V \).
Step 4: Final Answer:
The voltmeter reading will decrease.
(b)
Step 1: Detailed Explanation:
The reading of the voltmeter corresponds to the terminal voltage \( V = E - Ir \).
Every cell has a small internal resistance (\( r \)). When current \( I \) flows through the circuit, some energy is consumed in moving charges against this internal resistance, leading to an internal potential drop of \( Ir \).
As the rheostat decreases external resistance to increase current, this internal drop \( Ir \) rises, leaving less potential difference available at the external terminals of the cell.
Step 2: Final Answer:
The increase in current leads to a higher potential drop (\( Ir \)) inside the cell, which reduces the terminal potential difference (\( V \)).