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A circuit shown in the figure has resist...

A circuit shown in the figure has resistances `20 Omega` and `30 Omega`. At what value of resistance `R_x` will the thermal power generated in it be practically independent of small variations of that resistance? The voltage between points `A` and `B` is supposed to be constant in this case.

Text Solution

Verified by Experts

The correct Answer is:
`12 omega`

The equivalent resistance between the points is
`R_(0) = R_(1) + (R_(2) R_(x))/(R_(2) + R_(x))`
Power generated by `R_(x) is I_(x)^(2) R_(x)`.
From fig. `S 7.3`, `I = ((V)/( R_(1) + ( R_(2)R_(x))/( R_(2) + R_(x))))`
` I_(x) = ((V)/( R_(1) + ( R_(2)R_(x))/( R_(2) + R_(x))))((R^(2))/( R_(2) + R_(x)))`
`P_(x) = I_(x)^(2) R_(x) = [(VR_(2))/( R_(1) R_(2) + R_(1) R_(x) + R_(2) R_(x))]^(2) R_(x)`
For the maximum value , `( dP_(x))/( dR_(x)) = 0 `
or `R_(1) R_(2) + R_(1) R_(x) + R_(2) R_(x) = 2( R_(1) + R _(2)) R_(x)`
or `R_(x) = ( R_(1) R_(2))/( R_(1) + R_(2)) = ( 20 xx 30)/( 20 + 30) = 12 Omega`
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A circuit shown in Fig, has resistances R_(1) = 20 Omega and R_(2) = 30 Omega . At what value of the resitanace R_(x) will the thermal power generated in it practically independent of small variations of that resistance? The voltage between the points A and B is supposed to be constant in this case

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Knowledge Check

  • Consider the circuit shown in the figure. The value of the resistance X for which the thermal power generated in it is practically independent of small variation of its resistance is

    A
    `X=R`
    B
    `X=(R )/(3)`
    C
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    D
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  • In the circuit shown in figure the total resistance between points A and B is R_0 . The value of resistance R is

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    `R_0`
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    `sqrt3R_0`
    C
    `R_0/2`
    D
    `R_0/sqrt3`
  • In the circuit shown in the figure, the current flowing in 2 Omega resistance

    A
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    B
    `1.2A`
    C
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    D
    `1.0A`
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