Question
The resistance of a metal is given by $$R = \frac{V}{I},$$ where $$V$$ is potential difference and $$I$$ is the current. In a circuit the potential difference across resistance is $$V = \left( {8 \pm 0.5} \right)V$$ and current in resistance, $$I = \left( {2 \pm 0.2} \right)A.$$ What is the value of resistance with its percentage error ?
A.
$$4\Omega \pm 16.25\% $$
B.
$$\left( {4 \pm 0.7} \right)\Omega $$
C.
$$4\Omega \pm 0.7\% $$
D.
$$4\Omega \pm 7\% $$
Answer :
$$4\Omega \pm 16.25\% $$
Solution :
$$\eqalign{
& {\text{Actual}}\,R = \frac{8}{2} = 4 \cr
& \% \,{\text{error}}\,{\text{in}}\,R = \% \,{\text{error}}\,{\text{in}}\,V + \% \,{\text{error}}\,{\text{in}}\,I \cr
& = \frac{{0.5}}{8} \times 100\% + \frac{{0.2}}{2} \times 100\% = 16.25\% \cr
& R = 4\Omega \pm 16.25\% \cr} $$