The resistance R - - where V-100 - 5 volts and - -10 - 0-3 amperes- Calculate the percentage error in R-

As given: R=V/I Using formula for relative error: Δ R/R=Δ V/V+Δ I/I Here, V=100 V, Δ V=5 V and I=10 A, Δ I=0.3 A Δ R/R=5/100+0.3/10 Δ R/R=0.05+0.03=0.08 Perce ...

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Byju's Answer

Standard XII

Physics

Multiplication & Division of Errors

The resistanc...

Question

The resistance $R = \frac{V}{I}$ , where $V = 100 \pm 5$ volts and $I = 10 \pm 0.3$ amperes. Calculate the percentage error in $R$ .

8 %

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10 %

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12 %

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14 %

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Solution

The correct option is A 8 %
As given:
$R = \frac{V}{I}$
Using formula for relative error:
$\frac{Δ R}{R} = \frac{Δ V}{V} + \frac{Δ I}{I}$

Here, $V = 100 V, Δ V = 5 V$ and
$I = 10 A, Δ I = 0.3 A$

$\frac{Δ R}{R} = \frac{5}{100} + \frac{0.3}{10}$
$\frac{Δ R}{R} = 0.05 + 0.03 = 0.08$
Percentage Error:
$\frac{Δ R}{R} \times 100 = 8$ %

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The resistance R=VI, where V=100±5 volts and I=10±0.3 amperes. Calculate the percentage error in R.

The correct option is A 8 %As given: R=VI Using formula for relative error: ΔRR=ΔVV+ΔII Here, V=100 V, ΔV=5 V and I=10 A, ΔI=0.3 A ΔRR=5100+0.310 ΔRR=0.05+0.03=0.08 Percentage Error: ΔRR×100=8 %

The resistance $R = \frac{V}{I}$ , where $V = 100 \pm 5$ volts and $I = 10 \pm 0.3$ amperes. Calculate the percentage error in $R$ .