Question

The voltage across a lamp is V =(6.0+_ 0.1) v and the current passing through it is ( 4+-0.2) A ? Find the power consumed?

Answer 1

Power = VI

P = 6*4 = 24 Watt

dP = P(dV/V + dI/I)
dP = 24*(0.1/6 + 0.2/4)
dP = 1.6

Power consumed = (24 ± 1.6) Watt

Answer 2

The power consumed by the lamp is, $\bold{P=(24 \pm 1.6) W}$

Solution:

Power consumed by lamp $P=V \times I \quad \rightarrow(1)$

Here, V is the original voltage and I is the original current.

So, as per the question, V= 6 V and I = 4 A.

Hence, power $P=6 \times 4=24 W$

In order to find the error, differentiate equation (1),

$\Rightarrow \Delta P=\Delta V \times I+V \times \Delta I \quad \rightarrow(2)$

Now divide (2) by (1)

$\Rightarrow \frac{\Delta P}{P}=\frac{\Delta V \times I}{V \times I}+\frac{V \times \Delta I}{V \times I}$

$\Rightarrow \frac{\Delta P}{P}=\frac{\Delta V}{V}+\frac{\Delta I}{I}$

$\Rightarrow \Delta P=\left(\frac{\Delta V}{V}+\frac{\Delta I}{I}\right) \times P \quad \rightarrow(3)$

Substitute, $\bold{P=24 W, V=6 V, I=4 A, \Delta V=0.1 V \text { and } \Delta I=0.2 A}$ in (3)  

$\Rightarrow \Delta P=\left(\frac{0.1}{6}+\frac{0.2}{4}\right) \times 24$

$\Rightarrow \Delta P=1.6 W$

Thus, the power consumed by the lamp is,

$P=(24 \pm 1.6) W$