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Current Electricity

Question
CBSEENPH12039080

Using Kirchhoff’s rules determine the value of unknown resistance R in the circuit so that no current flows through 4  resistance. Also find the potential difference between A and D.

Solution

Applying Kirchhoff's loop rule for loop ABEFA,
              –9 + 6 + 4 × 0 + 2I = 0

                                          I = 1.5 A                                           … (i)

For loop BCDEB,

3 + IR + 4 × 0 – 6 = 0

Therefore,        IR = 3
Putting the value of I from equation (i), we have
3 over 2 cross times R space equals space 3
rightwards double arrow space space straight space straight R straight space equals straight space 2 straight capital omega

Potential difference between A and D through path ABCD,
9 straight space – straight space 3 straight space – straight space IR straight space equals straight space straight V subscript AD straight space end subscript
rightwards double arrow straight space 9 straight space – straight space 3 straight space – straight space 3 over 2 cross times straight space 2 straight space equals straight space straight V subscript AD
rightwards double arrow space space space space space space space space space space space space space space space space space straight V subscript AD straight space equals straight space 3 straight space straight V

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