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.
Show 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.
(a) How will the voltmeter reading change?
The voltmeter reading will decrease. (b) Justification: Step 1: Understanding the Measurement:
The voltmeter connected in parallel across the cell measures the terminal voltage (\(V\)) of the cell. Step 2: The Terminal Voltage Formula:
The terminal voltage (\(V\)) of a cell is related to its electromotive force (e.m.f. or \(E\)) and internal resistance (\(r\)) by the equation:
\[ V = E - Ir \]
where \(I\) is the current drawn from the cell. The term \(Ir\) represents the potential drop across the internal resistance of the cell, often called "lost volts". Step 3: Analyzing the Change:
The problem states that the current (\(I\)) in the circuit is increased (by adjusting the rheostat).
According to the equation \(V = E - Ir\):
- \(E\) (the e.m.f. of the cell) is a constant.
- \(r\) (the internal resistance) is a constant.
- As the current \(I\) increases, the product \(Ir\) (the lost volts) also increases.
- Since we are subtracting a larger value (\(Ir\)) from a constant value (\(E\)), the resulting terminal voltage (\(V\)) must decrease.
