Why does adding a second lamp in parallel not make both lamps dimmer?

Because in parallel each lamp gets the full supply voltage, regardless of how many others are connected. Adding another branch does not take anything away from the first one.

In series it would. That contrast is the whole topic.

The two rules that generate everything

In series, there is one path. Current is the same everywhere, and the supply voltage is shared between the components.

In parallel, there are branches. Each branch gets the full voltage, and the current splits between them.

Almost every circuit question is an application of one of those two lines. Write them at the top of your working.

Why the lamps stay bright

Two lamps in parallel across a 6 V supply: each has 6 V across it. Each therefore draws the same current it would have drawn on its own, and lights just as brightly.

Two lamps in series across the same 6 V supply: they share it, 3 V each. Less voltage means less current means dimmer. Adding a third makes it worse again.

This is why house lighting is wired in parallel. It is also why one bulb failing leaves the rest working — the other branches still have a complete path, whereas in series a single break stops everything.

The part that catches people out

If each parallel branch draws its own current, then adding branches increases the total current drawn from the supply. More current is leaving the battery, not the same amount redistributed.

So the total resistance of a parallel combination is less than the smallest individual resistance. Students expect adding components to increase resistance, and in parallel it does the opposite — you have added another route for charge to take.

Two 10 Ω resistors in parallel give 5 Ω. In series they give 20 Ω. Same two components, four times the difference.

The practical consequence: a battery runs down faster with more parallel lamps, and the real reason a circuit has a fuse is that total current can climb as more is switched on.

Working a question

Find what is the same first, then what is shared.

For a series circuit, find the total resistance, use V = IR to get the single current, then find each voltage from that current and each resistance.

For a parallel circuit, start from the voltage — every branch has the supply voltage — then find each branch current separately and add them for the total.

Choosing which of those two routes to take is most of the work. Getting it right depends only on correctly identifying which quantity is shared and which is common, so decide that before touching a formula.