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mash [69]
4 years ago
12

A 100 W, 250 V lamp is connected in parallel with a resistance R across a supply voltage of 250 V. The total power in the circui

t is 1100 W. Find the value of R
Physics
1 answer:
Rudiy274 years ago
7 0

Answer:

62.5 \Omega

Explanation:

First of all, we calculate the resistance of the lamp. The power of the lamp is given by

P=\frac{V^2}{R'}

Where

P = 100 W is the power

V = 250 V is the voltage

R' is the resistance of the lamp

Solving for R',

R'=\frac{V^2}{P}=\frac{250^2}{100}=625 \Omega

Now this resistance is connected in parallel to the other resistance R, so their equivalent resistance is

\frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{R'} (1)

Now the total power in the circuit is

P = 1100 W

And the voltage is

V = 250 V

So we can write

P=\frac{V^2}{R_{eq}}

to find the equivalent resistance:

R_{eq}=\frac{V^2}{P}=\frac{250^2}{1100}=56.8 \Omega

Therefore, rearranging (1), we find R:

\frac{1}{R}=\frac{1}{R_{eq}}-\frac{1}{R'}=\frac{1}{56.8}-\frac{1}{625}=0.016 \Omega^{-1} \rightarrow R=62.5 \Omega

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