Electrical circuits

Candidates learn that series resistors add, then wrongly assume parallel ones do too. A parallel branch gives the current an extra route, so more current flows for the same p.d. and the combined resistance is less than the smallest single resistor. Two equal resistors $R$ in parallel give $R/2$; $6\ \Omega$ with $3\ \Omega$ gives $2\ \Omega$.

Lamps that must be controlled separately -- household lighting is the stock example -- go in parallel, each on its own branch with the full supply p.d. Drawn in series, one switch or one broken lamp turns them all off, and the lamps share the supply p.d. so each is dimmer. Marks also go for using the correct standard symbols and drawing a complete closed loop.

A very common belief is that the first lamp "uses up" some current, so later components get less. In a series circuit there is only one path, so the current is the same at every point -- an ammeter reads the same wherever it is placed in the loop. What the components share in series is the potential difference, not the current.

In a parallel circuit the branch currents add up to the current from the source, so the source current is larger than the current in any one branch. Candidates instead quote one branch reading as the supply current, or take an average of the branches. The greater current flows in the lower-resistance branch, not equally through both.

In series, $V_\text{supply} = V_1 + V_2 + \ldots$ -- with a 12 V supply and 7 V across the first resistor, the second has $12 - 7 = 5$ V, not 12 V. In parallel, every branch has the same p.d., equal to the p.d. across the whole combination -- so branch p.d.s must not be added. Swapping the two rules, or adding p.d.s in a parallel circuit, is the frequent error.

Current is conserved at a junction: the total flowing in equals the total flowing out. If 1.2 A enters and one branch takes 0.8 A, the other carries $1.2 - 0.8 = 0.4$ A; if two branches leave carrying 0.5 A and 0.3 A, then 0.8 A arrived. Candidates add the branch to the input instead of subtracting, or assume the current splits equally between the branches.

An ammeter goes in series, in the loop carrying the current it measures; a voltmeter goes in parallel, across the component whose p.d. is wanted. Swapping them is treated as a fatal circuit error. Placing the ammeter in one branch of a parallel circuit is a subtler trap -- it then reads only that branch, not the total current supplied by the battery.