Circuits — series, parallel and potential dividers
Building circuits
- Real gadgets are circuits built from a handful of components, wired in two basic ways.
- Get the rules for series and parallel and you can predict any simple circuit.
- We finish with a clever trick: the potential divider.
Components to know
- cell / battery — drives the current; a switch breaks or completes the circuit.
- resistor (fixed) and variable resistor (to control the current).
- fuse — melts if the current is too big; diode / LED — current one way only (an LED also lights).
- thermistor — resistance falls as it gets hotter; LDR — resistance falls as light gets brighter.
What happens to the resistance of a thermistor as it gets hotter?
A thermistor's resistance falls as temperature rises — useful in temperature-sensing circuits.
Series circuits
- The parts form one single loop.
- The current is the same at every point.
- The supply p.d. is shared between the components.
- Resistors in series add up: $R_{\text{total}} = R_1 + R_2 + \dots$
A $3.0\ \Omega$ and a $5.0\ \Omega$ resistor are connected in series. What is the total resistance, in Ω?
In series, resistances add: $R = 3.0 + 5.0 = 8.0\ \Omega$.
In a series circuit, the current is:
There is only one path, so the same current flows through every component in a series circuit.
Parallel circuits
- The parts are on separate branches.
- Each branch gets the full supply p.d.; the current splits between branches.
- The total resistance is less than the smallest single resistor: $\dfrac{1}{R_{\text{total}}} = \dfrac{1}{R_1} + \dfrac{1}{R_2}$
- Home lamps are wired in parallel — each gets full voltage, and one failing leaves the others on.
A $6.0\ \Omega$ and a $3.0\ \Omega$ resistor are connected in parallel. What is the total resistance, in Ω?
$\dfrac{1}{R} = \dfrac{1}{6.0} + \dfrac{1}{3.0} = \dfrac{1}{6} + \dfrac{2}{6} = \dfrac{3}{6}$, so $R = 2.0\ \Omega$ — less than the smallest resistor.
Why are the lamps in a house wired in parallel?
In parallel each lamp gets the full supply p.d., and a break in one branch does not stop the others.
Potential dividers
- Two resistors in series share the supply voltage — a potential divider.
- The bigger resistor takes the bigger share of the voltage:
- Use a thermistor or LDR as one resistor and the output voltage changes with temperature or light — perfect for switching a heater or lamp on automatically.
Two equal resistors are in series across a $12\ \text{V}$ supply. What is the p.d. across one of them, in V?
Equal resistors share the voltage equally: each gets $\dfrac{12}{2} = 6\ \text{V}$.
You've got it
- series: one loop, same current everywhere, p.d. shared, $R_{\text{total}} = R_1 + R_2$
- parallel: branches, each gets full p.d., current splits, $\dfrac{1}{R_{\text{total}}} = \dfrac{1}{R_1} + \dfrac{1}{R_2}$
- thermistor: R falls when hot · LDR: R falls in bright light
- potential divider: two series resistors share the voltage by their ratio