Question

The circuit shown in figure, contains a battery, a rheostat and two identical lamps. What will happen to the brightness of the lamps if the resistance of the rheostat is increased?

• A.

  	Lamp P	Lamp Q
  (a)	Less brighter	Brighter

• B.

  	Lamp P	Lamp Q
  (d)	No change	Brighter

• C.

  	Lamp P	Lamp Q
  (c)	Brighter	Less brighter

• D.

  	Lamp P	Lamp Q
  (b)	Less brighter	Less brighter

Answer 1

The correct option is A

	Lamp P	Lamp Q
(a)	Less brighter	Brighter

Consider two extreme cases.
$\bullet$ When the resistance of the rheostat is zero whole current will pass through the rheostat such that the current through $Q$ is zero or $Q$ will be short circuited. The circuit is then essentially a battery in series with lamp P and lamp $P$ will glow brightly.
$\bullet$ When the resistance of the rheostat is increased slightly some current starts flowing through the lamp $Q.$ Thus it starts glowing very dim.

When the resistance of the rheostat is increased considerably the current in the lamp $Q$ and rheostat section moves through the lamp $Q$ owing to increased resistance in the rheostat path. It is the case of a series connection involving lamp $P,$ lamp $Q$ and the battery. This new voltage drop alongside the lamp $Q$ will reduce the voltage drop along lamp $P.$ Thus the lamp $P$ gets less bright and the lamp $Q$ brightens.
Hence, option $\left(a\right)$ is correct.