Resistors in Series & Parallel (OCR Gateway GCSE Physics)

Resistors in Series

• When two or more resistors are connected in series, the total (or combined) resistance is equal to the sum of their individual resistances
• For example, for three resistors of resistance R_1, R₂ and R₃, the total resistance can be calculated using:

• Where R is the total resistance, in Ohms (Ω)
• Increasing the number of resistors increases the overall resistance, as the charge now has more resistors to pass through
• The total voltage is also the sum of the voltages across each of the individual resistors
  • In a series circuit, the voltage of the power supply is shared between all components

Three resistors connected in series. The total voltage is the sum of the individual voltages, and the total resistance is the sum of the three individual resistances

Resistors in Parallel

• When two or more resistors are connected in parallel, the total (or net / combined) resistance decreases
• In the below circuit, the combined resistance of the resistors R₁ and R₂ is less than if they were connected in series

Two resistors connected in parallel. The total resistance is less than if they were connected in series

• This happens because each resistor creates an extra path along which the charge can flow
  • This allows more charge to flow overall
  • This leads to a smaller overall resistance

• The advantages of this kind of circuit are:
  • The components can be individually controlled, using their own switches
  • If one component stops working the others will continue to function

ANSWER:  C

Step 1: Write down the equation for the combined resistance in series

R = R₁ + R₂ + R₃

Step 2: Substitute the values for total resistance R and the other resistors

60 Ω = 30 Ω + R₂ + 10 Ω

Step 3: Rearrange for R₂

R₂ = 60 Ω – 30 Ω – 10 Ω = 20 Ω

Part (a)

Step 1: Recall that current is conserved in a series circuit

• • Since current is conserved in a series circuit, it is the same size if measured anywhere in the series loop
  • This means that since the cell supplies 2 A to the circuit, current is 2 A everywhere
  • Therefore, 2 A flows through the fixed resistor

Part (b)

Step 1: List the known quantities

• • Current I = 2 A
  • Resistance R = 4 Ω

Step 2: State the equation linking potential difference, resistance and current

• • The equation linking potential difference, resistance and current is:

V = IR

Step 3: Substitute the known values into the equation and calculate the potential difference

V = 2 × 4 = 8 V

• • Therefore, the voltmeter reads 8 V across the fixed resistor