Potential Divider

A potential divider is a circuit in which resistors, thermistors or LDRs are used to provide a variable potential difference. Examples in everyday life include audio volume controls or freezer temperature controls.

Two resistors are able to divide the potential difference which is being supplied to them from a cell. The resistance values of the resistors dictates the proportion of potential difference they will receive.

V_out = (V_in R₁) / (R₁ + R₂)

In which:

• V_in = potential difference supplied by the cell
• V_out = potential difference across the relevant resistor
• R₁ = resistance of the relevant resistor, R₁
• R₂ = resistance of resistor R₂

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Electromotive Force and Internal Resistance

The energy which is provided by a cell of battery per coulomb charge flowing through it is known as the electromotive force (? or emf). This figure is equal to the potential difference across the terminals of the cell when there is no current.

? = E / Q

In which:

• ? = electromotive force in volts (V)
• E = energy in joules (J)
• Q = charge in coulombs (C)

Batteries and cells possess an internal resistance (r). This is measured in ohms (?). As electricity flows round a circuit the internal resistance of the cell resists the current flow. Therefore, it can be seen that the thermal energy is wasted by the actual cell.

? = I (R + r)

• ? = electromotive force in volts (V)
• I = current in amperes (A)
• R = resistance of the load in the circuit in ohms (?)
• r = internal resistance of the cell in ohms (?)

It is possible to rearrange this equation:

? = IR + Ir

Followed by:

? = V + Ir

In the above equation IR is replaced by V which is the terminal potential difference. This is measured in volts (V) and is the potential difference across the terminals of the cell when there is a current flowing around the circuit. It is always lower then the emf of the cell.

A graph of terminal potential difference against current

When the terminal potential difference (V) is plotted against the current in the circuit (I) the result is a straight line with a negative gradient.

The emf equation can be rearranged to match the expression for a straight line: y = mx + c.

• ? = V + Ir
• ? – Ir = V
• V = -Ir + ?
• V = -rI + ? which matches y = mx + c

From the above equation you can now see that:

• the y-axis intercept is equal to the emf of the cell
• the gradient of the graph is equal to the internal resistance of the cell (-r)