Circuit Combinations

Circuit Combinations

There are two ways to wire components together: in a single loop (series) or on separate branches (parallel). The two behave very differently. Learn how current, potential difference and resistance act in each, work out for yourself why parallel resistance falls rather than being told it does, and you can read any circuit.

Series and parallel

Four rows, and the last one is the reason almost everything in your house is wired the second way:

Total resistance in series

A 3 Ω resistor and a 5 Ω resistor are connected in SERIES. What is the total resistance in ohms (Ω)?

Which are true?

Select ALL THREE statements that are TRUE.

• In a series circuit the potential differences across the components must add up to the supply p.d.
• In a parallel circuit the branch currents add up to the current drawn from the supply
• Two identical lamps in series each glow more dimly than one lamp alone would
• In a parallel circuit the potential difference is shared out between the branches
• In a series circuit the current is largest nearest the positive terminal, because it is used up as it goes round
• Adding another resistor always increases the total resistance of a circuit

One branch at a time

A 12 V supply is connected across two 6 Ω resistors in PARALLEL. Each branch has the full supply p.d. across it. What is the current in ONE branch, in amps (A)? (Use I = V ÷ R.)

Now the whole circuit

Both branches carry 2 A, so the supply delivers 4 A in total at 12 V. What is the TOTAL resistance of the circuit, in ohms (Ω)? (Use R = V ÷ I.)

Why did it fall?

Two 6 Ω resistors in parallel came out at 3 Ω, which is lower than either of them on its own. What is the best explanation?

• The second branch gives the charge another route, so at the same supply p.d. a larger total current flows, and a larger current at the same p.d. means a smaller total resistance
• The p.d. is shared between the two resistors, so each one only has to resist half as much
• The two resistances partly cancel each other out
• Splitting the current means each resistor carries less, so each behaves as a smaller resistance

Adding more resistors

The two arrangements pull the total resistance in opposite directions, and now you know why: • Add a resistor in series → total resistance increases. One route, and it just got longer. • Add a resistor in parallel → total resistance decreases. Another route, so more current flows for the same p.d. Worth a sanity check every time: a parallel total must come out smaller than the smallest branch. If your answer is bigger than one of the resistors you have started with, you have used the series rule by mistake.

What does each observation tell you?

Why your lights are not in series

Old decorative light strings really were wired in series, and anyone who owned a set remembers the consequence: one bulb fails and the entire string goes dark, with no way to tell which one it was except by replacing them one at a time. It was not a mistake. Series wiring is cheaper, needs no thick supply cable, and the mains p.d. is divided between all the bulbs, so each one can be a low-voltage bulb. The manufacturer traded reliability for cost. Household lighting makes the opposite trade. Every lamp is on its own parallel branch, so each gets the full mains p.d., each can be switched independently, and a failed bulb in the kitchen leaves the hall alone.

Wiring a house

You are explaining domestic wiring to someone. Four questions come up.

• Why are the sockets and lights in a house wired in parallel rather than in series?
• Somebody plugs in a second heater, on its own socket. What happens to the total resistance of the household circuit and to the current drawn from the supply?
• So why can you not simply keep plugging in more appliances?
• A single faulty appliance blows the fuse and everything on that circuit stops. Does that mean the house is wired in series after all?

Order the method

Put the steps for measuring the resistance of a component in a circuit in order.

• Connect the component to a cell to make a complete circuit
• Put an ammeter in series to measure the current I
• Put a voltmeter in parallel across the component to measure the p.d. V
• Calculate the resistance with R = V ÷ I

The circuit rules

In a series circuit the current is the _____ everywhere, the potential difference is shared, and the total resistance is the _____ of the resistors. In a parallel circuit the potential difference is the same across every _____, the current splits, and the total resistance is _____ than the smallest single resistor.

Explain the opposite effects

Exam practice. In about 50 words, explain why adding a lamp in PARALLEL lowers a circuit's total resistance while adding one in SERIES raises it. Include:

• what adding a parallel branch does to the number of routes available to the charge
• what happens to the total current at the same supply p.d. in each case
• how R = V ÷ I turns that change in current into a change in total resistance