Circuits: Current, Resistance and Potential Difference
Electric Current and Charge
Electric current is the flow of charge carriers through a conductor. In metals, these charge carriers are electrons that move through the wire when a voltage is applied.
Current is measured in amperes (A) and represents the amount of charge flowing past a point per second. The equation is \(I = \frac{Q}{t}\) where I is current, Q is charge in coulombs, and t is time in seconds.
Current is measured using an ammeter, which must be connected in series with the component you want to measure. This ensures all the current flows through the ammeter.
Potential Difference
Potential difference (also called voltage) is the driving force that pushes current around a circuit. It represents the energy transferred per coulomb of charge.
The equation for potential difference is:
$$V = \frac{W}{Q}$$
Where V is potential difference in volts, W is work done (energy transferred) in joules, and Q is charge in coulombs.
Potential difference is measured using a voltmeter. Unlike an ammeter, a voltmeter must be connected in parallel with the component. This allows it to measure the energy difference between the two points without affecting the current flow.
Think of potential difference like the height difference in a waterfall — the greater the height difference, the more energy each drop of water has when it reaches the bottom.
Resistance and Ohm's Law
Resistance opposes the flow of current in a circuit. Different materials and components have different resistances — metals have low resistance while insulators have very high resistance.
Ohm's Law states that \(V = I \times R\) where V is potential difference in volts, I is current in amperes, and R is resistance in ohms (Ω). This relationship only applies to ohmic conductors at constant temperature.
You can rearrange Ohm's law to find any of the three quantities:
$$I = \frac{V}{R} \text{ and } R = \frac{V}{I}$$
The resistance of a wire depends on four factors: its length (longer = higher resistance), cross-sectional area (thicker = lower resistance), material (different metals have different resistivity), and temperature (higher temperature usually = higher resistance for metals).
Some components like filament bulbs are non-ohmic — their resistance changes with temperature, so they don't follow Ohm's law exactly.
Series Circuits
In a series circuit, components are connected end-to-end in a single loop. Current has only one path to follow.
In series circuits: current is the same everywhere (\(I_1 = I_2 = I_3\)), potential difference is shared between components (\(V_{total} = V_1 + V_2 + V_3\)), and total resistance equals the sum of individual resistances (\(R_{total} = R_1 + R_2 + R_3\)).
If one component fails in a series circuit, the whole circuit stops working because the current path is broken. This is why old Christmas lights used to all go out when one bulb failed.
Parallel Circuits
In a parallel circuit, components are connected on separate branches. Current can follow multiple paths.
In parallel circuits, each component receives the full supply voltage. This is why household appliances are connected in parallel — each device gets the full 230V regardless of what other appliances are switched on.
In parallel circuits: potential difference is the same across each branch (\(V_1 = V_2 = V_3\)), total current equals the sum of branch currents (\(I_{total} = I_1 + I_2 + I_3\)), and total resistance is less than the smallest individual resistance.
The formula for total resistance in parallel is: \(\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\)
Electrical Power
Electrical power is the rate of energy transfer in a circuit. It tells us how quickly electrical energy is being converted to other forms like heat, light or motion.
The basic power equation is:
$$P = V \times I$$
Where P is power in watts, V is potential difference in volts, and I is current in amperes. By combining this with Ohm's law, we get two more useful equations: \(P = I^2R\) and \(P = \frac{V^2}{R}\).