# Potential Divider Circuits

## Potential Divider Circuits Revision

**Potential Divider Circuits**

A **potential divider** circuit is a series of **resistors** connected to a fixed power supply which is capable of splitting the input **voltage** into a fraction of the voltage. This is particularly useful for circuits where the power input is needed to supply several components with different **potential differences**.

**Potential Dividers with Fixed Resistors**

A **potential divider **circuit can be seen below. This circuit is made of a power source Vin and two fixed **resistors**. It also has a **power** output across R_1.

The **potential divider** circuit works by splitting the input **voltages** between the two **resistors** in a ratio of their resistances. For example, if both resistors were the same value for **resistance**, each would get half of the share of the input voltage.

An equation can be used to calculate the output **voltage** in circuits like the one above. This is not on your data sheet so worth noting and remembering:

V_{\text{out}}=\dfrac{R_1}{R_t}\times V_{\text{in}}

The equation can be adjusted so that the top value for **resistance** is the **resistor** of which the output voltage is over.

**Example:** Calculate the voltage output across the 200 \Omega resistor.

**[2 marks]**

\begin{aligned} \bold{V}_{\textbf{out}} &= \bold{\dfrac{R_1}{R_2} \times V}_{\text{in}} \\ &= \dfrac{200}{200+700} \times 6 \\ &= \bold{1.33} \textbf{ V} \end{aligned}

We can do a quick logical check of this. The smaller resistor will always receive the smallest share of the input voltage. So our answer looks good as R_1 is much smaller than R_2 so will only receive a small share of the input voltage.

**Variable Resistors**

For the output of a **potential divider **circuit to be variable, **variable resistors**, **LDRs** and **thermistors** may be included in the circuit. This is particularly useful if you want the circuit to control an outcome such as a light switching on or a fan switching on.

The circuit above includes a **thermistor**. Remember, a thermistor is a **variable resistor** whose resistance depends upon the temperature. As the temperature increases, the **resistance** decreases.

**Example: **In this potential divider circuit, what would happen to R_1, R_2 and V_{\text{out}} as the temperature of the thermistor increases?

**[3 marks]**

Firstly, as the temperature increases, \bold{R_2}** decreases**.

As R_1 is a fixed resistor, its **resistance remains the same.**

Finally, as R_2 has decreased, R_1 is now a larger part of the ratio of resistances and will therefore, receive a larger proportion of the input voltage. So \bold{V}_{\textbf{out}} **increases.**

## Potential Divider Circuits Example Questions

**Question 1:** What is the purpose of a potential divider circuit?

**[2 marks]**

A Potential divider circuit is used to **divide the input voltage in a circuit into smaller fractions of the voltage**. This may be to **supply multiple components that require a smaller voltage than the input voltage**.

**Question 2:** Calculate the output voltage in this potential divider circuit.

**[2 marks]**

**Question 3:** The potential divider circuit is used in a room which varies in temperature between 25 \degree C and 50 \degree C. At 25 \degree C, the resistance of the thermistor is 10 \text{ k} \Omega which decreases to 800 \, \Omega at 50 \degree C. What is the minimum and maximum output voltage from this circuit?

**[3 marks]**

At 25 \degree C:

\begin{aligned} \bold{ V}_{\textbf{out}} &= \bold{\dfrac{R_1}{R_2} \times V}_{\textbf{in}} \\ &= \dfrac{5 \times 10^3}{10 \times 10^3 + 5 \times 10^3} \times 12 \\ &= \bold{4} \textbf{ V}\end{aligned}

At 50 \degree C:

\begin{aligned}V_{\text{out}} &= \dfrac{R_1}{R_2} \times V_{\text{in}} \\ &= \dfrac{5000}{800+5000} \times 12 \\ =& \bold{10.3} \textbf{ V} \end{aligned}Therefore the minimum output voltage is 4 \text{ V} at 25 \degree C and the maximum output voltage is 10.3 \text{ V} at 50 \degree C.

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