Today we will discuss three multiple choice questions which appeared in IIT-JEE 2010 question paper:

**(1)** Consider a thin square sheet of side *L* and thickness t, made of a material of resistivity *ρ*. The resistance between two opposite faces, shown by the shaded areas in the figure is

(A) directly proportional to *L *

(B) directly proportional to *t*

(C) independent of *L*

(D) independent of *t*

We have *R *= *ρL/A* where *A* is the cross section area which is equal to* L t*.

Therefore, *R *= *ρL/Lt = ρ/t*, which is independent of *L *[Option (C)].

**(2)** Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances R_{100}, R_{60} and R_{40} respectively, the relation between these resistances is :

(A) 1/R_{100} = 1/R_{40} + 1/R_{60}

(B) R_{100} = R_{40} + R_{60}

(C) R_{100} > R_{60} > R_{40}

(D) 1/R_{100} > 1/R_{60} > 1/R_{40}

The power *P* dissipated in a resistance *R* is given by

*P* = *V*^{2}/*R* where *V* is the voltage applied across the resistance.

This shows that the resistance of the filament is *smaller* if the wattage of the incandescent lamp is *greater*. In other words, the reciprocal of the filament resistance is greater if the wattage of the incandescent lamp is *greater*. This is true at all temperatures including room temperature. Therefore we have

1/R_{100} > 1/R_{60} > 1/R_{40}

**(3)** To verify Ohm's law, a student is provided with a test resistor R_{T}, a high resistance R_{1}, a small resistance R_{2}, two identical galvanometers G_{1} and G_{2}, and a variable voltage ource V. The correct circuit to carry out the experiment is

To verify Ohm’s law, the current through R_{T} is to be measured by connecting an *ammeter in* *series* with it and the voltage across R_{T} is to be measured by connecting a *voltmeter in* *parallel* with it. One galvanometer is to be converted into an ammeter by connecting the small resistance R_{2} across it. The other galvanometer is to be converted into a voltmeter by connecting the high resistance R_{1} in series with it. So the correct circuit to carry out the experiment is the one shown in option (C).

You will find some multiple choice questions (with solution) on direct current circuits here.

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