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Consider a circuit having resistances 16 Ω and 30 Ωis excited by a voltage V. A variable resistance R is connected across the 16 Ω resistance. The power dissipated in 30 Ω resistance will be maximum when value of R is __________
  • a)
    30 Ω
  • b)
    16 Ω
  • c)
    9 Ω
  • d)
    0
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider a circuit having resistances 16 and 30 is excited by a volta...
We know that,
When R = 0, circuit current = V/30A
And Power dissipated = V2/30 Watts.
This is the maximum possible value which occurs for R = 0 Ω.
Free Test
Community Answer
Consider a circuit having resistances 16 and 30 is excited by a volta...
Resistance is given by:

P = V^2/(16+R+30)

To find the value of R for which the power dissipated in 30 is maximum, we need to differentiate P with respect to R and equate it to zero:

dP/dR = -V^2/(16+R+30)^2 + V^2/(16+R+30)^2 = 0

Simplifying, we get:

V^2/(16+R+30)^2 = V^2/(46+R)^2

(16+R+30)^2 = (46+R)^2

256 + 32R + R^2 + 900 = 2116 + 92R + R^2

60R = 960

R = 16

Therefore, the value of R for which the power dissipated in 30 is maximum is 16 .
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Consider a circuit having resistances 16 and 30 is excited by a voltage V. A variable resistance R is connected across the 16 resistance. The power dissipated in 30 Ω resistance will be maximum when value of R is __________a)30 Ωb)16 Ωc)9 Ωd)0Correct answer is option 'C'. Can you explain this answer?
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