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  • (a) Three resistors are connected in parallel and the combination is connected to a battery, ammeter, voltmeter and key. Draw suitable circuit d

(a) Three resistors R_1, R_2 and R_3 are connected in parallel and the combination is connected to a battery, ammeter, voltmeter and key. Draw suitable circuit diagram and obtain an expression for the equivalent resistance of the combination of the resistors.

(b) Calculate the equivalent resistance of the following network : 

 

 

 

 
 
 
 
 

Answers (1)

 

Total current , I= I_{1}+I_{2}+I_{3}

Assume that 'R_{p}' be the equivalent resistance ofR_1, R_2, R_3

Total current , I = \frac{V}{R_{p}}

On applying Ohm’s law for each resistor R_1, R_2, R_3

I_{2}= \frac{V}{R_{1}}, I_{2}=\frac{V}{R_{2}}, I_{3}= \frac{V}{R_{3}}

I = I_{1}+I_{2}+I_{3}

I = \frac{V}{R_{1}}+\frac{V}{R_{2}}+\frac{V}{R_{3}}

\therefore I = V\left (\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}} \right )= \frac{V}{R_{p}}

\therefore \frac{1}{R_{p}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}

(b)

\frac{1}{R_{p}}=\frac{1}{20}+\frac{1}{120}=\frac{1}{10}

R_{p}= 10 \Omega

Equivalent resistance of the network = R_{eq}= R_{1}+R_{p} = 10 +10 = 20\Omega

Posted by

Sumit Saini

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