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Using Kirchhoff's rules determine the va...

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

Text Solution

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Apply Kirchoof.s Voltage rule For loop ABEA
`-9 + 6 + 4 xx 0 + 2 I =0`
`2I -3 =0`
`I = 3/2 = 1. 5 A`
For loop ABCED
`3 + IR + 4 xx 0-6 =0`
`therefore IR =3`
Substituting the value of current I,
`3/2 xx R =3 `
`therefore R = 2Omega`
Potential difference between A & D through path ABCD:
`+ 9V - 3 V - IR = V _(AD)`
`+ 9- 3 - 3/2 xx 2 = V _(AD)`
` implies V _(AD) =3 V`
Alternatively, through path AFD
`3/2 xx 2 = V _(AD)`
`implies V _(AD) = 3 V`
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