$(a)$ Nichrome wire of length $L^{\prime}$ and radius ${ }^{\prime} R^{\prime}$ has resistance of $10\, \Omega$. How would the resistance of the wire change when

$(i)$ only length of the wire is doubled ?

$(ii)$ only diameter of the wire is doubled ? Justify your answer.

$(b)$ Why element of electrical heating devices are made$-$up of alloys ?

Solution

$(i)$ $R \propto L$

So resistance becomes two times,

i.e. $R=2 \times 10=20 \Omega$

$(ii)$ $R \propto \frac{1}{ A } \propto \frac{1}{ D ^{2}}$

So when diameter is doubled, resistance becomes $\frac{1}{4}$. of its original,

i.e. $R=10 / 4=2.5 \Omega$

$(b)$ This is because alloys do not oxidise readily at high temperature.

A nichrome wire has a resistance of $10\, \Omega$. Find the resistance of another nichrome wire, whose length is three times and area of cross-section four times the first wire.

Medium

Medium

Easy

Easy

Easy