# How to Calculate and Solve Potential Divider Problems

A potential divider circuit is arranged in such a way to get an output voltage from a battery of particular e.m.f.

For a potential divider, the current through the each resistor is the same because they are arranged in series.

**Potential Divider derivation**

Using Ohms law,

The effective resistance is = R_{1} + R_{2 }

V_{in} = IR

I = V_{in}/ (R_{1} + R_{2 })

The Voltage across R1 will be,

V_{1} = IR_{1}

Since I = V_{in}/ (R_{1} + R_{2 })

V_{1} = V_{in}/ (R_{1} + R_{2 }) x R_{1}

V_{1} = R_{1}/(R_{1} + R_{2 }) x V_{in}

For voltage across R_{2}

V_{2} = R_{2}/(R_{1} + R_{2 }) x V_{in}

**Uses of Potential divider**

The circuits are often used in electronic circuits. They are useful when a sensor is connected to a processing circuits.

Temperature sensor

A common example of a sensing system is a temperature sensor in a thermostat, which uses a thermistor. The thermistor is then used in a potential divider as the diagram below. In the diagram, the potential difference is divided between the resistor and the thermistor. As the temperature rises, the resistance of the thermistor decreases, so the potential difference across it decreases and the potential difference across the resistor increases as the temperature increases.

**How to calculate in Potential divider circuits**

The first thing that must be done is to write down the formula

V_{out} = R_{2}/(R_{1} + R_{2 }) x V_{in
}

Then look at the question to know what you are asked to calculate.

Example 1

The diagram shows a potential divider circuit. The voltmeter has infinite resistance and the battery has negligible internal resistance.

The variable resistor is set on its maximum resistance of 200 Ω. Calculate the voltmeter reading.

Solution

V = 200 /(200 + 180) x 6

V = (200/380) x 6 = 3.16 v

Example 2

In the circuit shown, X is a variable resistor whose resistance can be changed from 5.0 Ω to 500 Ω. The e.m.f. of the battery is 12.0 V. It has negligible internal resistance.

What is the maximum range of values of potential difference across the output?

A 1.3 V to 11.1 V

B 1.3 V to 12.0 V

C 1.5 V to 11.1 V

D 1.5 V to 12.0 V

Solution

V_{out} = R_{2}/(R_{1} + R_{2 }) x V_{in }

The minimum resistance in variable resistor is 5Ω

V_{out} = 5/(5 + 40) x 12 = 1.3 v

The maximum resistance is 500Ω

V_{out} = 500/(500 + 40) x 12 = 11.1 v

The correct answer is A

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