State that, for a parallel circuit, the current from the source is larger than the current in each branch

Published by Patrick Mutisya · 8 days ago

Cambridge IGCSE Physics 0625 – Series and Parallel Circuits

4.3.2 Series and Parallel Circuits

Learning Objective

State that, for a parallel circuit, the current supplied by the source is larger than the current flowing in any individual branch.

Key Concepts

  • In a parallel circuit each branch is connected directly across the source, so every branch experiences the same potential difference (voltage).

  • The total current supplied by the source, \$I_{\text{total}}\$, is the algebraic sum of the currents in the individual branches:

    \$I{\text{total}} = I1 + I2 + I3 + \dots\$

  • Because each branch draws some current, the total current must be greater than the current in any single branch:

    \$I{\text{total}} > In \quad \text{for all } n.\$

  • Resistance of the whole parallel network is lower than the resistance of any single branch:

    \$\frac{1}{R{\text{eq}}}= \frac{1}{R1}+ \frac{1}{R2}+ \frac{1}{R3}+ \dots\$

Why the Source Current Is Larger

Consider a parallel circuit with two branches, each containing a resistor \$R1\$ and \$R2\$ respectively, connected to a battery of emf \$V\$.

  1. Each branch sees the full battery voltage \$V\$.

  2. The current in each branch is given by Ohm’s law:

    \$I1 = \frac{V}{R1}, \qquad I2 = \frac{V}{R2}.\$

  3. The source must supply both currents simultaneously, so

    \$I{\text{total}} = I1 + I2 = \frac{V}{R1} + \frac{V}{R_2}.\$

  4. Since both terms are positive, \$I{\text{total}}\$ is necessarily larger than either \$I1\$ or \$I_2\$ alone.

Comparison: Series vs Parallel

FeatureSeries CircuitParallel Circuit
Current through each componentSame throughout the circuit (\$I{\text{total}} = I1 = I_2 = \dots\$)Different in each branch; \$I{\text{total}} = I1 + I_2 + \dots\$
Voltage across each componentDivides according to resistance (\$V{\text{total}} = V1 + V_2 + \dots\$)Same across each branch (all experience the source voltage \$V\$)
Equivalent resistance\$R{\text{eq}} = R1 + R_2 + \dots\$ (greater than any individual \$R\$)\$\displaystyle\frac{1}{R{\text{eq}}}= \frac{1}{R1}+ \frac{1}{R_2}+ \dots\$ (less than any individual \$R\$)
Source current compared to branch currentsSource current equals the current in each component.Source current is larger than the current in any single branch.

Worked Example

Calculate the total current supplied by a 12 V battery connected to two parallel resistors, \$R1 = 6\ \Omega\$ and \$R2 = 12\ \Omega\$.

  1. Find the current in each branch:

    \$\$I_1 = \frac{12\ \text{V}}{6\ \Omega}=2\ \text{A},\qquad

    I_2 = \frac{12\ \text{V}}{12\ \Omega}=1\ \text{A}.\$\$

  2. Sum the branch currents:

    \$I{\text{total}} = I1 + I_2 = 2\ \text{A} + 1\ \text{A}=3\ \text{A}.\$

  3. Observe that \$I{\text{total}} = 3\ \text{A}\$ is larger than either \$I1\$ or \$I_2\$ individually, confirming the principle.

Practice Question

Three resistors \$R1 = 4\ \Omega\$, \$R2 = 6\ \Omega\$, and \$R_3 = 12\ \Omega\$ are connected in parallel across a 9 V source. Calculate the current supplied by the source and state whether it is larger than the current in each branch.

Suggested Diagram

Suggested diagram: Parallel circuit showing a battery connected to three separate branches, each containing a resistor \$R1\$, \$R2\$, \$R3\$. Label the current in each branch (\$I1\$, \$I2\$, \$I3\$) and the total source current (\$I_{\text{total}}\$).