CBSE Class 12 Physics 2020 Outside Delhi Set 2 Paper

Question : 8 of 11

Marks: +1, -0

SECTION - B

A uniform wire is cut into three parts with their lengths in the ratio

2:3:6

. The ends of each of these three parts are connected across an ideal battery of

10\,\text{V}

. If a current of

5\,\text{A}

is drawn from the battery, find the initial resistance of the wire.

Solution:

Consider that the resistance of a wire is

R

So, the resistance of the three parts are

\;\frac{2}{11} R,\;\frac{3}{11} R

and

\;\frac{6}{11} R

, respectively.

They are now connected in parallel combination across a source of voltage.

So, the equivalent resistance

R_{\text{eq}}

\; \frac{1}{R_{\;\text{eq}\;}} \;=\; \frac{1}{\frac{2}{11}R} + \frac{1}{\frac{3}{11}R} + \frac{1}{\frac{6}{11}R}

\therefore \;\; R_{\;\text{eq}\;} = \frac{11}{R}

\; \text{ Current } \;\; = I = 5\,\text{A}

V\;=10\,\text{V}

Applying Ohm's law,

10\;=5 \times \frac{11}{R}

\therefore \;\; R\;=5.5\,\Omega

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