GCSE — physicsMedium5 min read

Series and Parallel Circuits

Rules for current and voltage in series and parallel; total resistance

Tutor AI Team
Tutor AI Team

# Series and Parallel Circuits — GCSE Physics

Circuits can be connected in two fundamental ways: series and parallel. Understanding the rules for current, voltage, and resistance in each type is essential for circuit analysis at GCSE.

1. Series Circuits

In a series circuit, components are connected one after another in a single loop. There is only one path for the current.

Rules for Series Circuits

Current: The current is the same everywhere in a series circuit. Itotal=I1=I2=I3=...I_{\text{total}} = I_1 = I_2 = I_3 = ...

Voltage: The total voltage is shared between the components. Vtotal=V1+V2+V3+...V_{\text{total}} = V_1 + V_2 + V_3 + ...

Resistance: The total resistance is the sum of all individual resistances. Rtotal=R1+R2+R3+...R_{\text{total}} = R_1 + R_2 + R_3 + ...

Adding more resistors in series increases the total resistance and decreases the current.

2. Parallel Circuits

In a parallel circuit, components are connected on separate branches. There are multiple paths for the current.

Rules for Parallel Circuits

Current: The total current is split between the branches. It adds up. Itotal=I1+I2+I3+...I_{\text{total}} = I_1 + I_2 + I_3 + ...

More current flows through the branch with less resistance.

Voltage: The voltage is the same across all branches. Vtotal=V1=V2=V3=...V_{\text{total}} = V_1 = V_2 = V_3 = ...

Resistance: The total resistance is less than the smallest individual resistance. 1Rtotal=1R1+1R2+1R3+...\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...

For two resistors in parallel: Rtotal=R1×R2R1+R2R_{\text{total}} = \frac{R_1 \times R_2}{R_1 + R_2}

Adding more resistors in parallel decreases the total resistance and increases the total current.

3. Comparison

Property Series Parallel
Current Same everywhere Splits between branches
Voltage Splits between components Same across all branches
Resistance Adds up (RT=R1+R2R_T = R_1 + R_2) Decreases (1/RT=1/R1+1/R21/R_T = 1/R_1 + 1/R_2)
If one component breaks Whole circuit stops Other branches still work
Brightness of lamps Dimmer with more lamps Same brightness

4. Why Homes Use Parallel Circuits

  • Each appliance gets the full mains voltage (230 V in the UK)
  • Appliances can be switched on and off independently
  • If one appliance fails, others continue to work
  • Each branch can have its own fuse for safety

Worked Example: Series Circuit

Problem

Question: Three resistors (4 Ω, 6 Ω, 10 Ω) are connected in series to a 12 V battery. Calculate: (a) total resistance, (b) current, (c) voltage across the 6 Ω resistor.

(a) RT=4+6+10=20R_T = 4 + 6 + 10 = 20 Ω (b) I=V/R=12/20=0.6I = V/R = 12/20 = 0.6 A (c) V=IR=0.6×6=3.6V = IR = 0.6 \times 6 = 3.6 V

Solution

Worked Example: Parallel Circuit

Problem

Question: Two resistors (6 Ω and 3 Ω) are connected in parallel to a 12 V battery. Calculate: (a) total resistance, (b) total current, (c) current through each resistor.

(a) RT=(6×3)/(6+3)=18/9=2R_T = (6 \times 3)/(6 + 3) = 18/9 = 2 Ω (b) IT=V/R=12/2=6I_T = V/R = 12/2 = 6 A (c) I1=12/6=2I_1 = 12/6 = 2 A, I2=12/3=4I_2 = 12/3 = 4 A. Check: 2+4=62 + 4 = 6 A ✓

Solution

Worked Example: Mixed Circuit

Problem

Question: A 4 Ω resistor is in series with a parallel combination of 6 Ω and 3 Ω. The battery is 10 V. Calculate the current from the battery.

Parallel part: RP=(6×3)/(6+3)=2R_P = (6 \times 3)/(6+3) = 2 Ω Total: RT=4+2=6R_T = 4 + 2 = 6 Ω I=10/6=1.67I = 10/6 = 1.67 A

Solution

Worked Example: Finding Unknown Values

Problem

Question: In a series circuit with a 6 V battery, the voltage across one resistor is 2.5 V and across a second is 1.5 V. Calculate the voltage across a third resistor.

V3=6−2.5−1.5=2.0V_3 = 6 - 2.5 - 1.5 = 2.0 V

Solution

6. Practice Questions

    1. Two resistors (8 Ω and 12 Ω) are connected in series to a 10 V battery. Calculate the current. (2 marks)
    1. Two identical 20 Ω resistors are connected in parallel. Calculate the total resistance. (2 marks)
    1. In a parallel circuit, the total current is 3 A. One branch carries 1.2 A. What current flows through the other branch? (1 mark)
    1. A 12 V battery is connected to three lamps in series. Each lamp has a resistance of 4 Ω. Calculate: (a) total resistance, (b) current, (c) voltage across each lamp. (4 marks)
    1. Explain why adding a resistor in parallel to an existing circuit decreases the total resistance. (3 marks)

    Answers

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Frequently Asked Questions

Why does total resistance decrease in parallel?

Adding a parallel branch adds another path for current. More paths = less overall opposition = lower resistance.

Do real circuits use both series and parallel?

Yes! Most real circuits are combinations. For example, a string of Christmas lights might be in series, but the different strings are in parallel.

Summary

  • Series: one path; same current; voltage shared; RT=R1+R2R_T = R_1 + R_2
  • Parallel: multiple paths; current splits; same voltage; 1/RT=1/R1+1/R21/R_T = 1/R_1 + 1/R_2
  • Homes use parallel circuits for independence and full voltage
  • Adding series resistance increases RTR_T; adding parallel decreases RTR_T
Tags:
#gcse#physics#electricity#series#parallel#circuits#resistance

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