2018 A/L Physics Past Paper · Question 26 (English Medium)

Answer: (2) C only.

What the question asks

There are three conditions: (A), (B) and (C).

In each one, check this. Do all the unburnt bulbs glow with the same brightness?

Relevant theory

Passive resistors are those resistors in which the electrical energy flowing through them gets completely converted into heat.

If a number of resistors are connected so that they maintain the same potential difference

The bulbs are identical. So the brightness of a bulb depends only on its current.

Equal current means equal brightness. No current means no light.

Bulbs 1 and 2 are in parallel. Then come two branches in parallel: 3–4 and 5–6.

Reading the options

Each option is a set of conditions.

Check (A), (B) and (C) one at a time. Then pick the option.

Reasoning and calculation

Bulb 2 burnt

Bulb 2 is burnt. So bulb 1 carries all the current $I$.

The two branches share $I$. So 3, 4, 5 and 6 each carry $\frac{I}{2}$.

Bulb 1 has twice the current. It glows 4 times as bright. So (A) is false.

A

Bulbs 2 and 5 burnt

Bulbs 2 and 5 are burnt. The 5–6 branch is open.

Bulbs 1, 3 and 4 are in series. They carry the same current and glow equally.

But bulb 6 is not burnt and gets no current. It does not glow. So (B) is false.

B

No bulb burnt

No bulb is burnt. Bulbs 1 and 2 share $I$. Each carries $\frac{I}{2}$.

Each branch has resistance $2R$. So the branches also share $I$ equally. 3, 4, 5 and 6 each carry $\frac{I}{2}$.

All six bulbs carry the same current. They glow equally. So (C) is true.

C

$R_{total} = \frac{R}{2} + \frac{2R \times 2R}{2R + 2R}$

$\tfrac{3R}{2}$

$R_{total} = \frac{R}{2} + R$

$I_{bulb} = \frac{I}{2}$

In (A) the current does not split equally. Bulb 1 gets $I$. The others get $\frac{I}{2}$.

In (B) bulb 6 does not glow at all.

Only (C) is true.

Why the other options fail

In (B) bulb 6 does not glow. This option also leaves out (C).

In (A) bulb 1 carries twice the current of the others. So they do not glow equally.

(B) is false. Bulb 6 does not glow.

(A) and (B) are both false.

Conclusion

Only in (C) do all six bulbs carry the same current and glow equally.

The answer is option (2).

Explore

Six identical bulbs. Bulbs 1 and 2 are in parallel. Then come two branches, 3–4 and 5–6.

Bulb 2 burns out. Now bulb 1 carries all the current. It glows brighter than 3, 4, 5 and 6.

Bulb 5 burns out too. The 5–6 branch is open. Bulb 6 goes dark, though it is not burnt.

Now no bulb is burnt. Every bulb carries half the current. All six glow the same.

Only in C do all the bulbs glow equally. So the answer is option (2).