Two metallic wires of the same material have same length but cross-sectional area is in the ratio 1 : 2. They are connected (i) in series and (ii) in parallel. Compare the drift velocities of electrons in the two wires in both the cases (i) and (ii).

Solution

Let, the drift velocities of the wires be v_dand v_d' respectively.
Area of cross- section of two wires be A and A'.

Then,
A : A' = 1:2

This implies,
A' = 2A

i) When the two wires are connected in series, the same amount of current flows through both the wires.
Implies,
n A v_d e = n A' v_d' e
where,
n is the number of electrons per unit volume and,
e is the charge on electron.
Therefore,

$\frac{v_{d}}{{v_{d}}^{'}} = \frac{A'}{A} = \frac{2 A}{A} = 2 : 1$
ii) When the two wires are connected in parallel, the potential difference across the two wires would be the same.

Then,

$n A V_{d} e ρ \frac{l}{A} = n A' v_{d}' e ρ \frac{l}{A'}$

where, $ρ$ is the resistivity of the two wires.
Therefore,
$\frac{v_{d}}{{v_{d}}^{i}} = 1$

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Current Electricity

Two metallic wires of the same material have same length but cross-sectional area is in the ratio 1 : 2. They are connected (i) in series and (ii) in parallel. Compare the drift velocities of electrons in the two wires in both the cases (i) and (ii).

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