Question

A resistance of 5 ohm is connected in series with a parallel combination of R ohm and 10 ohm the total power consumed by the circuit is 1200 w . The applied voltag is 100v.find R

Answer 1

Answer:

       R = 5Ω

Explanation:

R Ω and 10 Ω In parallel

Resistance in parallel

= 1 / Rp = 1 / R + 1 / 10

1 / Rp = R + 10 / 10R

Rp = 10R / 10 + R

Rp and 5Ω in series

R' = 10R / 10+R  + 5

R' = 10R + 5(10 + R) / 10 + R

R' = 10R + 50 + 5R / 10 + R

R' = 15R + 50 / 10 + R ------{i}

Power(P) = 1200w  ,  Voltage(V) = 100V

P = V² / R

R' = V² / P

R' = 100 × 100 / 1200

R' = 100 / 12 Ω

R' = 25 / 3 Ω ------{ii}

from {i} and {ii}

15R + 50 / 10 + R = 25 / 3

3(15R + 50) = 25(10 + R)

45R + 150 = 250 + 25R

45R - 25R = 250 - 150

20R = 100

R = 100 / 20

R = 5Ω

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