Potential Dividers

Definition

A potential divider is a voltage divider, which make use of the voltage drop across resistors in series to divide voltage

PhysicsDefinitions

current is same at every point in a series circuit.
let this current be $I$ . Then P.D across resistors $R_{1}$ and $R_{2}$ would be given by $I R_{1}$ and $I R_{2}$ respectively.

Since sum of the p.d. in a series circuit is equal to the potential difference across the whole circuit. $V_{S} = I R_{1} + I R_{2} - - - - (1)$ $I = \frac{1}{R _{1} + R _{2}} V_{s} - - - - (2)$ $V = I R_{1}$

Substitute (1) into (2) $V_{1} = \frac{R _{1}}{R _{1} + R _{2}} V_{s}$

The term $\frac{R _{1}}{R _{1} + R _{2}}$ is a proper fraction and has a value less than 1 Hence we can see that voltage $V_{1}$ is a fraction of the supply voltage $V_{s}$

Likewise since: $V_{2} = I R_{2}$ $V_{2} = \frac{R _{2}}{R _{1} + R _{2}} V_{s}$

Hence both $V_{1}$ and $V_{2}$ are fractions of the supply voltage and the fractions are determined by the choice of resistors $R_{1}$ and $R_{2}$

In the potential divider circuit → if we replace resistors $R_{1}$ and $R_{2}$ with a potentiometer → a continuous range of voltages for $V_{1}$ and $V_{2}$ can be obtained.

larger values of $V_{2}$ can be obtained by increasing $R_{2}$ and vice versa

Example

example with circuit with potentiometer is found in the volume control knob of a radio or an electric guitar as shown in figure. circuit is also called variable potential divider.

With potentiometer → potential differences $V_{1}$ and $V_{2}$ follow the same formula: $V_{1} = \frac{R _{1}}{R _{1} + R _{2}} V_{s} an d V_{2} = \frac{R _{2}}{R _{1} + R _{2}} V_{s}$

Ratio of resistances can also be expressed → in terms of length of the resistor or rheostat or the angle of turns of a potentiometer slider.

since $R_{1}$ is proportional to $I$ , $V_{1}$ and $V_{2}$ may be expressed as: $V_{1} = \frac{I _{1}}{I _{1} + I _{2}} V_{s}$ $V_{2} = \frac{I _{2}}{I _{1} + I _{2}} V_{s} w h ere I_{1} an d I_{2} a re e q u i v i l an t l e n g t h s o f R_{1} an d R_{2}$

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Potential Dividers

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