Two questions from direct current circuits appeared in the IIT-JEE 2008 question paper. Here are those questions:

_{1}, R

_{2}and R

_{3 }connected to 3 V battery. If the power dissipated by the configurations R

_{1}, R

_{2}and R

_{3}are P

_{1}, P

_{2}and P

_{3}respectively, then

(a) P_{1 }> P_{2} > P_{3}

(b) P_{1 }> P_{3} > P_{2}

(c) P_{2 }> P_{1} > P_{3}

(d) P_{3 }> P_{2} > P_{1}

For the configuration R_{1},_{ }the central 1 Ω resistor can be ignored since it is connected between equipotential points (similar to the galvanometer in a balanced Wheatstone bridge). The equivalent resistance connected across the battery is therefore 1 Ω. [2 Ω in parallel with 2 Ω].

The equivalent resistance in the configuration R_{2} is 0.5 Ω. [2 Ω, 2 Ω and 1 Ω in parallel]

The equivalent resistance in the configuration R_{3} is 2 Ω.

Since power P = V^{2}/R we have P_{2 }> P_{1} > P_{3} [Option (c)].

The second question which follows is *Reasoning Type* with 4 choices out of which ** only one** is correct

STATEMENT-1

**and**

STATEMENT-2

Resistance of a metal increases with increase in temperature.

(A) STATEMENT-1 is True, STATEMENT-2 **is** a correct explanation for STATEMENT-1

(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 **is NOT** a correct explanation for STATEMENT-1

(C) STATEMENT-1 is True, STATEMENT-2 is False

(D) STATEMENT-1 is False, STATEMENT-2 is True

We have *R*/*X* = *l*_{1}/*l*_{2}

If the unknown resistance X is *decreased *on increasing its temperature, the null point can be obtained at the sme point as before by decreasing the value of the standard resistance. You should note that nothing is mentioned about the nature of the unknown resistance. It can be a negative temperature coefficient (of resistance) device such as a thermistor. So, statement 1 is true.

Metals have positive temperature coefficient of resistance. So, statement 2 is true. But it is not a correct explanation for statement-1.

The correct option is (B).

[If the unknown resistance is a metallic wire such as copper wire or nichrome wire, the resistance will increase on heating and the correct option will then be (D).