Potential divider

A potential divider consists of an 8.0 \Omega resistor, R, in series with a 12.0 \Omega resistor and a 6.0 V power supply.

Calculate:

• the current

• the p.d. across each resistor

• Calculating the current:

  • Total resistance = 12.0 \Omega + 8.0 \Omega = 20.0 \Omega
  • V=IR -> I=\frac{V}{R}=\frac{6.0 V}{20.0 \Omega}=0.30 A

• Calculating the p.d. across each resistor:

  • I=0.30 A
  • R_1=12.0 \Omega:
    • V_1=IR_1=0.30 A \times 12.0 \Omega=3.6 V
  • R_2=8.0 \Omega:
    • V_2=IR_2=0.30 A \times 8.0 \Omega=2.4 V
  • Check that they add back up to the EMF:
    • V_1 + V_2 = 3.6 V + 2.4 V = 6.0 V

What if one of the resistors is variable?

• If one resistor can change, the ratio of resistances will change.
• This will then change the p.d. across each resistor.
• This is useful in sensors - e.g. an LDR or thermistor.

A potential divider consists of an 8.0 \Omega resistor, R, in series with a thermistor and a 6.0 V power supply. Calculate the p.d. across R at each temperature.

The thermistor has a resistance of 16.0 \Omega at 20°C and 6.0 \Omega at 100°C.

• At 20°C:
  • R_{total} = 8.0 \Omega + 16.0 \Omega = 24.0 \Omega
  • I=\frac{V}{R}=\frac{6.0 V}{24.0 \Omega}=0.25 A
  • V_R=IR=0.25 A \times 8.0 \Omega=2.0 V
• At 100°C:
  • R_{total} = 8.0 \Omega + 6.0 \Omega = 14.0 \Omega
  • I=\frac{V}{R}=\frac{6.0 V}{14.0 \Omega}=0.43 A
  • V_R=IR=0.43 A \times 8.0 \Omega=3.4 V