Edexcel A Level (IAL) Physics-2.46 Electromotive Force- Study Notes- New Syllabus

Electromotive Force (e.m.f.), Internal Resistance and Terminal Potential Difference

Cells and power supplies provide energy to a circuit, but real sources are not ideal. They have an internal resistance that affects the voltage delivered to the external load.

 Electromotive Force (e.m.f.) — Definition

The e.m.f. \( \mathcal{E} \) of a source is the energy supplied per unit charge by the source when no current is flowing.

\( \mathcal{E} = \dfrac{W}{Q} \)

• Units: volts (V)
• It is the maximum possible voltage the cell can supply.
• Measured when the circuit is open (no current drawn).

 Internal Resistance \( r \)

Every cell or power supply has some resistance inside it due to its construction. This is called internal resistance.

• Causes a voltage drop inside the cell.
• Energy is lost as heat inside the cell.
• Reduces the terminal voltage when current flows.

Voltage lost inside cell:

\( V_{\text{lost}} = Ir \)

Terminal Potential Difference (t.p.d.)

The terminal potential difference \( V \) is the voltage available across the external circuit when current is flowing.

\( V = \mathcal{E} – Ir \)

Thus:

• Terminal p.d. is always less than the e.m.f. when current flows.
• The greater the current, the larger the internal voltage loss \( Ir \), and the smaller the t.p.d.
• If no current flows (\( I = 0 \)) → \( V = \mathcal{E} \).

Distinguishing e.m.f. and Terminal p.d.

Circuit Equation Including Internal Resistance

For a source with internal resistance \( r \) and external load \( R \):

\( \mathcal{E} = V + Ir \)

And since \( V = IR \):

\( \mathcal{E} = IR + Ir = I(R + r) \)

Using Graphs to Determine \( r \) and \( \mathcal{E} \)

Plot terminal voltage \( V \) against current \( I \):

• Straight line of form \( V = -rI + \mathcal{E} \)
• Gradient = \( -r \)
• Y-intercept = \( \mathcal{E} \)