Physics / Cell EMF & Internal Resistance
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EXPERIMENT 47 · PHYSICS LABORATORY

Internal Resistance and Electromotive Force of a Cell: Terminal Voltage and Load Characteristics

To determine the electromotive force (EMF) and internal resistance of an electrochemical primary cell by measuring terminal potential difference as a function of load current, evaluate the short-circuit current and maximum power transfer, and investigate instrument loading effects. Explore a virtual apparatus, collect readings and analyse a graph.

CHANGE · OBSERVE · MEASURE

Your virtual workbench.

TERMINAL VOLTAGE V—
MEASUREMENT STATUS

Ready for a virtual observation.

150.0 mA
Open-circuit electromotive force ℰ = 1.5000 V (calibrated against Weston standard cadmium cell)

Adjust the apparatus, then take a reading.

Timing is generated from the model; a short on-screen trial represents a longer physical interval. Animation is illustrative.

Simulation assumptions and limits

Model calculations assume constant ambient temperature (20.0 °C), negligible battery heating, and ideal linear Butler-Volmer kinetics without irreversible chemical degradation or deep discharge hysteresis. Real secondary and primary cells exhibit transient polarization relaxation times (τ ~ 5 to 30 s), non-linear Butler-Volmer overpotentials at very high discharge rates, and finite internal thermal capacitance.

Know your apparatus.

Primary Electrochemical Cell

Provides a stable chemical electromotive force (nominal open-circuit EMF ℰ = 1.500 V) with an inherent internal electrolytic and polarization resistance (r = 2.500 Ω) arising from finite ionic mobility in the ammonium chloride / zinc electrolyte paste.

Precision Decade Resistance Box

Provides calibrated non-inductive standard load resistances from 2.0 Ω to 50.0 Ω (tolerance ±0.1%), allowing smooth and repeatable adjustment of the external circuit current without introducing reactive impedance.

High-Impedance Digital DC Voltmeter

Measures the terminal potential difference V across the cell output posts with 0.001 V resolution and an input impedance exceeding 10 MΩ to ensure that voltmeter loading current is strictly negligible (< 0.15 μA).

Low-Resistance Precision DC Ammeter

Measures the closed-loop load current I from 0.0 mA to 350.0 mA with 0.1 mA resolution, engineered with a low-burden shunt resistance (R_A ≤ 0.05 Ω) to minimize insertion voltage drops.

Single-Pole Low-Resistance Knife Switch

Closes and opens the discharge circuit intermittently with negligible contact resistance (< 5 mΩ), preventing prolonged cell discharge and minimizing thermal heating or cumulative polarization during observation intervals.

Heavy-Gauge Copper Connecting Leads

Forms robust low-resistance electrical interconnections between circuit components with total lead resistance under 0.02 Ω, ensuring that all measured potential drops represent the cell and intended load.

FOLLOW THE METHOD

A reason behind every step.

To determine the electromotive force (EMF) and internal resistance of an electrochemical primary cell by measuring terminal potential difference as a function of load current, evaluate the short-circuit current and maximum power transfer, and investigate instrument loading effects. Suggested independent settings: 50.0, 100.0, 150.0, 200.0, 250.0, 300.0 mA.

1

Open-Circuit Inspection and Baseline EMF Verification

Inspect the open-circuit cell using the high-impedance digital voltmeter with the main knife switch open; record the quiescent open-circuit terminal voltage to verify baseline electromotive force ℰ₀ = 1.500 V prior to drawing discharge current.

Why this step matters

Establishing the open-circuit EMF before current flow verifies the chemical integrity of the cell and confirms that zero initial polarization exists.

2

Closed-Loop Series Circuit and Kelvin Voltmeter Connections

Connect the circuit in series: primary cell positive terminal to ammeter input, ammeter output to the decade resistance box, and resistance box back to the cell negative terminal through the knife switch. Connect the high-impedance voltmeter directly across the cell battery posts (Kelvin voltage sensing configuration) to exclude lead resistance drops.

Why this step matters

Kelvin 4-wire potential sensing ensures that the voltmeter measures the true terminal voltage across the cell electrodes, completely bypassing ohmic drops along the high-current connecting wires.

3

Initial High-Resistance Load Setting and Current Reading

Set the decade resistance box to its highest load setting (producing minimum initial current I = 50.0 mA). Momentarily close the knife switch for 3 to 5 seconds, read both the ammeter current I and the digital voltmeter terminal potential difference V, and immediately open the switch to prevent chemical exhaustion or polarization buildup.

Why this step matters

Starting at minimum current limits initial chemical consumption, while brief 3 to 5 second pulses prevent cumulative concentration polarization and internal Joule heating.

4

Chemical Relaxation Window and Stepwise Load Adjustment

Allow the cell a 60-second recovery period for ionic diffusion to re-establish chemical equilibrium at the electrode interfaces. Step down the load resistance progressively to draw currents of 100.0 mA, 150.0 mA, 200.0 mA, 250.0 mA, and 300.0 mA, recording the stabilized terminal voltage V at each setting.

Why this step matters

The 60-second recovery interval allows depolarizing agents to clear accumulated hydrogen films, ensuring each observation begins from identical equilibrium conditions.

5

Data Tabulation and Linear Regression Fitting

Tabulate the paired values of load current I (in amperes) and terminal potential difference V (in volts). Plot terminal voltage V on the vertical axis against current I on the horizontal axis; fit an ordinary least-squares straight line to determine the slope m and the vertical intercept b.

Why this step matters

Linear regression across multiple discharge levels averages out meter quantization noise and contact resistance fluctuations, yielding statistically robust fit parameters.

6

Parameter Extraction and Performance Bounds Calculation

Extract the internal resistance as r = −m and the true electromotive force as ℰ = b. Calculate the extrapolated short-circuit current I_sc = ℰ / r, evaluate the maximum deliverable external power P_max = ℰ² / (4r), and compare the fitted parameters against manufacturer reference specifications.

Why this step matters

Extrapolating from the linear regression determines the absolute physical operating bounds of the cell without requiring destructive short-circuit testing.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into a result.

See a complete example report ↗

Points are your observations. The fit uses SI x and y values before display scaling.

LINEAR FIT · y = mx + b
V = −r · I + ℰ; r = −m, ℰ = b
#Load current I (mA)Terminal voltage V (V)Load current I (A)Terminal voltage V (V)Remove

No readings yet. Take a virtual measurement and record it.

Calculate it yourself.

CHECK YOUR UNDERSTANDING

Explain what the measurements mean.

A voltmeter connected across an open-circuit battery reads 1.50 V. When a 5.00 Ω resistor is connected across the battery terminals, the voltmeter reading drops to 1.00 V. What is the internal resistance of the battery?

In a graph of terminal voltage V (y-axis) versus discharge current I (x-axis) for a real DC cell, what do the slope and y-intercept represent?

Under what load condition does a DC power source with internal resistance r deliver maximum electrical power to an external resistor R_load?

Why does warming a cold chemical battery generally improve its ability to deliver high currents to a load?