In an electrical circuit, the voltage is measured as and the current is measured as The value of the resistance is [2024]

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Solution

Q.
In an electrical circuit, the voltage is measured as $V = (200 \pm 4)$ $volt$ and the current is measured as $I = (20 \pm 0.2)$ $A .$ The value of the resistance is [2024]

1 $(10 \pm 4.2) Ω$

2 $(10 \pm 0.3) Ω$

3 $(10 \pm 0.1) Ω$

4 $(10 \pm 0.8) Ω$

Ans.
(2)

Given, voltage, $(V) = (200 \pm 4) V$

Current, $(I) = (20 \pm 0.2) A$

Resistance, $(R) = \frac{V}{I} = \frac{200}{20} = 10 Ω$

Now, error in $R$ is given by,

$\frac{Δ R}{R} = \frac{Δ V}{V} + \frac{Δ I}{I} = \frac{4}{200} + \frac{0.2}{20} = 0.03$

$∴$ $Δ R = R \times 0.03 = 10 \times 0.03 = 0.3 Ω$

So, the value of Resistance is $(10 \pm 0.3) Ω$

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