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(a) With the help of a suitable circuit diagram prove the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.

(b) In an electric circuit two resistors of $12\; \Omega$ each are joined in parallel to a 6 V battery. Find the current drawn from battery.

Answers (1)

(a) It is observed that total current $I$ is equaql to the sum not seperate current .

$I=I_{1}+I_{2}+I_{3}$ ___(i)

Let $R_{P}$ be the equivalent resistance of he parallel combination of resistance.

By applying Ohm's law , $I=\frac{V}{R_{P}}$ , _____(ii)

From (1) and (ii)

$\frac{V}{R_{P}}=\frac{V}{R_{1}}+\frac{V}{R_{2}}+\frac{V}{R_{3}}$

Cancel V from both sides

$\frac{1}{R_{P}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}$

Hence,if u resistance are connected in parallel, then the equivalent resistance of the circuit -

$\frac{1}{R_{eq}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}+----\frac{1}{R_{n}}$

(b) Given, Two resistors of $12\Omega$ connected in parallel.

$V=6V$

$\therefore \frac{1}{R_{eq}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$

$\frac{1}{R_{eq}}=\frac{1}{12}+\frac{1}{12}=\frac{2}{12}$

According to Ohm's law,

$V=IR$

$6=I\times 6$

$\frac{6}{6}=I$

$I=1\; amphere$

Posted by

Sumit Saini

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