Question

The voltage across a lamp is $(12.0\pm 0.1)$V and the current through it is $(2.0\pm 0.1)$A. The power consumed in it is

• A. 25.4 W
• B. 23.6 W
• C. 24.0 W
• D. 23.4 W

Answer 1

The correct option is C 24.0 W

$\begin{array}{c}\text{Given - voltage across the Lamp}=12.0\pm 0.1V\\ \text{Curent Drawn}=2.0\pm 0.1A\end{array}$

$\begin{array}{c}\text{we know power consume}\\ P=V\cdot I-\left(i\right)\end{array}$

$\begin{array}{c}\text{Taking Logarithm Both Sides in eq- (i)}\\ \Rightarrow \log P=\log V+\log I\end{array}$

$\begin{array}{c}\text{Differentiating both Sides.}\\ \begin{array}{cc}\frac{dP}{P}& =\frac{dV}{V}+\frac{dI}{I}\\ \Rightarrow \frac{dP}{P}& =\frac{0.1}{12}+\frac{0.1}{2}=\frac{0.7}{12}\end{array}\end{array}$

$\begin{array}{c}\text{and Power}P=V\cdot I=12\times 2=24W\\ \Rightarrow dP=24\times \frac{0.7}{12}=1.4\\ \Rightarrow \text{Power}P=24\pm 1.4W\\ \text{Without any error most accurate value is}\\ P=24W\text{.}\end{array}$