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
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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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