Recall and use in calculations, the fact that: (a) the sum of the currents entering a junction in a parallel circuit is equal to the sum of the currents that leave the junction (b) the total p.d. across the components in a series circuit is equal to

📌 Objective

Recall and use in calculations the following facts:

1. (a) The sum of the currents entering a junction in a parallel circuit equals the sum of the currents leaving the junction.
2. (b) The total potential difference (p.d.) across components in a series circuit equals the sum of the individual p.d.s across each component.
3. (c) The p.d. across an arrangement of parallel resistances is the same as the p.d. across one branch in that arrangement.

Think of a water pipe that splits into two smaller pipes. The amount of water that flows into the junction must equal the total amount that flows out.

Mathematically:

\$I{\text{in}} = I{\text{out}}\$

In a parallel circuit with two branches:

\$I{\text{total}} = I1 + I_2\$

Example: If a 12 V battery supplies 3 A into a junction, and one branch carries 1.5 A, the other branch must carry 1.5 A.

Imagine a chain of dominoes. The total height of the chain is the sum of the heights of each domino.

For a series circuit:

\$V{\text{total}} = V1 + V2 + \dots + Vn\$

Example calculation:

Think of a group of friends standing on a seesaw. Each friend experiences the same height relative to the ground, regardless of how many friends are on each side.

In a parallel arrangement:

\$V{\text{across each branch}} = V{\text{across the whole arrangement}}\$

Example: Two resistors, \$R1 = 4\,\Omega\$ and \$R2 = 6\,\Omega\$, are connected in parallel across a 12 V supply. Both branches see 12 V.

Current through each branch can be found using Ohm’s law:

\$I1 = \dfrac{V}{R1} = \dfrac{12}{4} = 3\,\text{A}\$

\$I2 = \dfrac{V}{R2} = \dfrac{12}{6} = 2\,\text{A}\$

Check with current conservation: \$I{\text{total}} = I1 + I_2 = 5\,\text{A}\$.

📝 Examination Tips

• Always sketch the circuit before calculating.
• Use the correct rule: add currents for junctions, add voltages for series, keep voltage constant for parallel.
• Check units: volts (V) for potential difference, amperes (A) for current, ohms (Ω) for resistance.
• Remember Ohm’s law: \$V = IR\$ and \$I = V/R\$.
• When in doubt, verify with Kirchhoff’s laws: current law (KCL) and voltage law (KVL).