JEE MAIN - Physics (2012 - No. 25)
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference
applied across it. If the percentage errors in the measurement of the current and the voltage difference
are 3% each, then error in the value of resistance of the wire is
6 %
zero
1 %
3 %
Explicação
We know R = $${V \over I}$$
$$\therefore$$ $${{\Delta R} \over R} = {{\Delta V} \over V} + {{\Delta I} \over I}$$
Percentage error in R =
$${{\Delta R} \over R} \times 100 = {{\Delta V} \over V} \times 100 + {{\Delta I} \over I} \times 100$$
$$\therefore$$ $${{\Delta R} \over R} \times 100 =$$ 3% + 3 % = 6%
$$\therefore$$ $${{\Delta R} \over R} = {{\Delta V} \over V} + {{\Delta I} \over I}$$
Percentage error in R =
$${{\Delta R} \over R} \times 100 = {{\Delta V} \over V} \times 100 + {{\Delta I} \over I} \times 100$$
$$\therefore$$ $${{\Delta R} \over R} \times 100 =$$ 3% + 3 % = 6%