Circuit Basics: Current, Potential Difference, & Resistance
Before diving into rules, you must command the definitions of the three key quantities of circuit calculations:
- Current ($I$, measured in Amperes, $A$): The rate of flow of electrical charge.
- Potential Difference ($V$, measured in Volts, $V$): The work done per unit charge (often called voltage).
- Resistance ($R$, measured in Ohms, $\Omega$): The measure of how hard it is for current to flow.
Ohm's Law links these three elements together in a crucial equation:
Rules of Series Circuits
A series circuit has only **one path** for current to flow. Think of it as a single loop. Here are the three non-negotiable rules for series calculations:
Current is the SAME everywhere
$$I_{total} = I_1 = I_2 = I_3$$
Potential Difference splits across components
$$V_{total} = V_1 + V_2 + V_3$$
Total Resistance is the sum of all resistors
$$R_{total} = R_1 + R_2 + R_3$$
Rules of Parallel Circuits
A parallel circuit contains **branches** or multiple loops. The current splits, but the potential difference remains constant across each parallel branch:
Potential Difference is the SAME across each branch
$$V_{total} = V_{branch 1} = V_{branch 2}$$
Current splits across branches
$$I_{total} = I_{branch 1} + I_{branch 2}$$
Worked Exam Example
Worked GCSE Example
Question: A $12\text{V}$ battery is connected in series with a $4\Omega$ resistor and a $2\Omega$ resistor.
1. Calculate the total resistance of the circuit.
2. Calculate the current flowing through the $4\Omega$ resistor.
Solution:
- Since the components are connected in series, we add their resistances: $$R_{total} = R_1 + R_2 = 4\Omega + 2\Omega = 6\Omega$$
- Use Ohm's Law ($V = I \times R$) to find the total current: $$I = \frac{V}{R_{total}} = \frac{12\text{V}}{6\Omega} = 2\text{A}$$
- Since it is a series circuit, the current is the same everywhere. Therefore, the current through the $4\Omega$ resistor is also $2\text{A}$.
Answers: Total Resistance = $6\Omega$, Current = $2\text{A}$.
Frequently Asked Questions
Adding resistors in parallel adds more loops/branches for the electric charge to flow through. Think of it like adding extra lanes to a highway; even if the new lanes have speed limits, the overall capacity increases, allowing more cars (current) to pass through, which corresponds to a lower overall resistance.
In a series circuit, if one bulb breaks, the entire circuit is broken and all bulbs go out. In a parallel circuit, each branch is independent; if a bulb on one branch breaks, bulbs on other branches will continue to shine because their loops are still complete.
Secure Your GCSE Physics Grade
Work 1-on-1 with elite UK physics tutors to tackle circuit math, force equations, and exam board papers. Build your custom schedule today.