Using Kirchoff’s rules determine the value of unknown resistance R i

1.	Using Kirchoff’s rules determine the value of unknown resistance R in the circuit so that no current flows through 4Ω resistance. Also find the potential difference between A and D.
Answer» 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 ∴ IR = 3 Putting the value of I from (i) we have \(\frac{3}{2}\times R=3\) \(\Rightarrow R=2\Omega\) Potential difference between A and D through path ABCD 9 - 3 - IR = VAD or 9 - 3 - \(\frac{3}{2}\times 2\) = V_AD \(\Rightarrow\) V_AD = 3V

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

Answer»

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

∴ IR = 3

Putting the value of I from (i) we have

\(\frac{3}{2}\times R=3\) \(\Rightarrow R=2\Omega\)

Potential difference between A and D through path ABCD

9 - 3 - IR = VAD

or 9 - 3 - \(\frac{3}{2}\times 2\) = V_AD \(\Rightarrow\) V_AD = 3V