Using Kirchoff's rules, calculate the current through the 40\; \Omega and 20\; \Omega resistors in the following circuit.

 
 
 

Answers (1)
  • According to Kirchoff's loop rule, The sum of potential differences across a closed loop is zero.

   

In ABCDA, applying Kirchoff's Loop Rule -

        80-20I_{1}-40I_{2}=0

        8-2I_{1}-4I_{2}=0

On rearranging, the equation we have, 

    I_{1}+2I_{2}-4=0 ___(1)

 In CDEFC, applying Kirchoff's Loop Rule -

    -40I_{2}-40+10 (I_{1}-I_{2})=0

    -40\; I_{2}-40+10\; I_{1}-10 \; I_{2}=0

    -50\; I_{2}-40+10\; I_{1}=0

On rearranging, the equation we have 

    I_{1}-5\; I_{2}-4=0 _____(2)

from (1) and (2)

    I_{1}-5\; I_{2}-4-I_{1}+2I_{2}-4=0

            7\; I_{2}=0

                I_{2}=0

On equaling the value of I_{2} in equation (1) , we get 

            I_{1}=4A

Hence, there is no current through  the 40\Omega resistor and 4A current flows through the 20\Omega resistor.

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