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In the electric ntework shown in the fig...

In the electric ntework shown in the figure, use Kirchhoffs rules to calculate the power consumed by the resistance `R = 4 Ω.`

Text Solution

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For loop ABCDA
`-12 + 2I _(1) + 4 ( I _(1) + I _(2)) =0`
`therefore 3I_(1) + 2I _(2) =6" "…(i)`
For loop ADFEA
`-4 ( I _(1) + I _(2)) + 6=0`
`therefore 2I _(1) + 2I_(2) =3" "…(ii)`
Solving (i) and (ii), we get
`I _(1) = 3 A`
`I _(2) =- 1. 5 A`
Hence, power consumed by the resistor
`R = ( I _(1) + I _(2)) ^(2) R`
`= (1.5) ^(2) xx 4 =9 ` watt
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