Two Karnataka CET 2010 Multiple Choice Questions on Direct Current Circuits

The following questions appeared in Karnataka CET 2010 question paper:

(1) A battery of e.m.f. E has internal resistance ‘r’. A variable resistance R is connected to the terminals of the battery. A current I is drawn from the battery. V is the terminal P.D. If R alone is graually reduced to zero, which of the following best describes I and V?

(a) I approaches zero, V approaches E

(b) I approaches E/r, V approaches zero

(c) I approaches E/r, V approaches E

(d) I approaches infinity, V approaches E

The current I is given by

I = E/(r+R)

When R is reuced to zero, I = E/r

Since the terminal P.D. is given by V = ER/(r+R), we have V = 0 when R = 0.

The correct option is (b).

(2) Three voltmeters A, B and C having resistances R, 1.5 R and 3 R respectively are used in a circuit as shown. When a P.D. is applied between X and Y, the readings of the voltmeters are V₁, V₂ and V₃ respectively. Then

(a) V₁ = V₂ = V₃

(b) V₁ <>2 = V₃

(c) V₁ > V₂ > V₃

(d) V₁ > V₂ = V₃

The effective resistance of the voltmeters B and C in parallel is 1.5R× 3R/(1.5R+3R) = R.

Therefore, the same P.D. exists across A and the parallel combination of B and C and the voltmeters show the same reading [Option (a)].