Two wires each of radius of cross section r but of different materials are connected together end to end (i.e. in series). If the densities of charge carriers in the two wires are in the ratio 1: 4, the drift velocity of electrons in the two wires will be in the ratio

Question

Two wires each of radius of cross section r but of different materials are connected together end to end (i.e. in series). If the densities of charge carriers in the two wires are in the ratio 1: 4, the drift velocity of electrons in the two wires will be in the ratio (A) 1: 2 (B) 2: 1 (C) 4: 1 (D) 1: 4

Tardigrade Admin · Accepted Answer

Two wires carry the same current I=n1 e A Vd1=n2 e A Vd2 So n1 Vd1=n2 Vd2 or (Vd1/Vd2)=(n1/n2)=4 ⇒ Vd1: Vd2=4: 1

Q. Two wires each of radius of cross section $r$ but of different materials are connected together end to end (i.e. in series). If the densities of charge carriers in the two wires are in the ratio $1 : 4$ , the drift velocity of electrons in the two wires will be in the ratio

$1 : 2$

$2 : 1$

$4 : 1$

$1 : 4$

Two wires carry the same current
$I = n_{1} e A V_{d_{1}} = n_{2} e A V_{d_{2}}$
So $n_{1} V_{d_{1}} = n_{2} V_{d_{2}}$
or $\frac{V _{d_{1}}}{V _{d_{2}}} = \frac{n _{1}}{n _{2}} = 4$
$\Rightarrow V_{d_{1}} : V_{d_{2}} = 4 : 1$

Q. Two wires each of radius of cross section r but of different materials are connected together end to end (i.e. in series). If the densities of charge carriers in the two wires are in the ratio 1:4, the drift velocity of electrons in the two wires will be in the ratio

1:2

2:1

4:1

1:4