An ideal V DC source feeds a two-branch circuit at junction P

PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity

Problem

An ideal

10\,

V DC source feeds a two-branch circuit at junction P. In branch 1, current

I_R

flows through a single

5\,\Omega

resistor and reaches junction Q. In branch 2, a controlled current source delivers a current

I_S

that is proportional to

I_R

according to

I_S = k I_R

, where

k

is a positive dimensionless constant less than

1

. The two branches merge at junction Q, and the combined current returns directly to the negative terminal of the source through ideal conductors. Assume all elements are ideal and that the indicated reference direction for

I_R

is away from the positive terminal of the source. (a) At junction P, relate

I_R

I_S

, and the current

I_{\text{source}}

leaving the positive terminal of the

10\,

V supply. (b) Using the given supply voltage and the

5\,\Omega

resistance, express

I_R

in terms of

k

. (c) Determine

I_{\text{source}}

as a function of

k

and show explicitly that

I_{\text{source}} = (1+k) I_R

. (d) Compute the power delivered by the controlled current source and the power dissipated in the resistor, both in terms of

k

. For what range of

k

(between

0

and

1

) does the controlled current source supply more power than the resistor dissipates? Justify your answer.

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