Voltage dividers
A voltage divider does exactly as its name suggests - it divides a supply voltage across two An electrical component that restricts the flow of electrical charge. Fixed-value resistors do not change their resistance, but with variable resistors it is possible to vary the resistance. which are connected in series.
The two resistors may have fixed values or one may be an LDR, a thermistor or other input device.
The supply voltage is divided in the ratio of the resistances in the voltage divider.
For the voltage divider shown:
\(\frac{{{V_1}}}{{{V_2}}} = \frac{{{R_1}}}{{{R_2}}}\)
\({V_s} = {V_1} + {V_2}\)
\({V_1} = {V_s} \times \frac{{{R_1}}}{{{R_1} + {R_2}}}\)
Of the three relationships stated above, any one can be used to find the voltage across a given resistor.
If one of the resistances in a voltage divider increases, then the voltage across that resistor also increases. This may appear to be the wrong way round but it is because of the way the resistors are connected together.
The circuit of a voltage divider may be drawn with the two resistors vertical, not horizontal. If there are two resistors in series across a voltage source, then the circuit is a voltage divider.
Question
A voltage divider consisting of two \(500 Ω\) resistors is connected across a \(9V\) battery. Calculate the voltage across one of the resistors.
\({V_1} = {V_s} \times \frac{{{R_1}}}{{{R_1} + {R_2}}}\)
\(= 9\times\frac{500}{500+500}\)
\(= 9 \times \frac{1}{2} = 4.5V\)
Voltage dividers are often used in transistor switching circuits.