Physics HL · Chapter 11: Current and Circuits
11.4 Terminal Potential Difference and the Potential Divider
Model real source behavior under load, place meters correctly, and predict divider output including loading effects.
Estimated time: 36 minutes
Ammeter and Voltmeter Placement Rules
An ammeter measures current through a component, so it must be connected in series with that component. A voltmeter measures potential difference across a component, so it must be connected in parallel across that component. Ideal ammeter resistance is zero; ideal voltmeter resistance is infinite.
Real instruments deviate from ideal values. A non-ideal voltmeter in parallel can draw current and change effective branch resistance, especially for high-resistance measurements. A non-ideal ammeter in series adds extra resistance and can reduce circuit current. Good experimental design includes estimating whether meter loading is negligible.
Terminal Potential Difference of a Real Cell
When current leaves the cell, internal resistance r causes an internal drop Ir so terminal voltage is below emf.
If no external current flows, I = 0 and terminal voltage equals emf. Under load, current rises and internal drop Ir increases, reducing terminal voltage available to the external circuit. This explains why battery voltage appears lower when powering demanding devices than when measured open-circuit.
Graphing terminal voltage V against current I gives a straight line with vertical intercept epsilon and gradient -r. This is a practical lab method for measuring emf and internal resistance from multiple load points.
Potential Divider Output and Loading
Unloaded divider output is a fixed fraction of supply set by resistor ratio.
A potential divider is a controlled voltage-sharing network. With no load attached to output, the ratio equation is exact. Once a load is attached, it forms a parallel combination with the lower divider resistor, reducing effective lower resistance and pulling output voltage down. This is divider loading.
To reduce loading error, design the next stage with input resistance much larger than divider output resistance, or use a buffer stage between divider and load. This is why practical sensor circuits often include high-input-impedance amplifier stages after resistive sensing networks.
Design Checks for Reliable Circuit Measurements
- Check whether voltmeter resistance is much larger than measured branch resistance.
- Check whether ammeter resistance is much smaller than branch resistance.
- For sources, separate open-circuit voltage from loaded terminal voltage.
- For dividers, compare no-load and loaded Vout before trusting calibration.
Simulation: Terminal Voltage and Loaded Divider
Explore V = epsilon - Ir under load and compare no-load vs loaded divider output to see measurement and design trade-offs.
Current
1.200 A
Terminal voltage
7.200 V
Load power
8.640 W
Efficiency
80.0 %
Vout (no load)
6.593 V
Vout (loaded)
5.070 V
Divider branch I
8.45e-3 A
Load current
3.38e-3 A
Terminal model follows V = emf - I r. Divider model compares open-circuit Vout to loaded Vout so you can see why low-output-resistance dividers are needed when the next stage draws current.
Test Yourself
A cell has emf 6.0 V and internal resistance 0.50 ohm. It is connected to an external resistor of 2.5 ohm. Enter the terminal potential difference in volts.
Hint: Find I from total resistance, then use V_terminal = epsilon - Ir.