current-electricity Question 30
Question: Q. 5. The following table gives the length of three copper wires, their diameters, and the applied potential difference across their ends. Arrange the wires in increasing order according to the following :
(i) The magnitude of the electric field within them,
(ii) The drift speed of electrons through them, and
(iii) The current density within them.
R] [CBSE SQP 2017-18]
| Wire No. | Length | Diameter | Potential Difference |
|---|---|---|---|
| 1 | $L$ | $3 d$ | $V$ |
| 2 | $2 L$ | $d$ | $V$ |
| 3 | $3 L$ | $2 d$ | $2 V$ |
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Solution:
Ans. (i)
$$ \begin{aligned} & E_{1}=\frac{V}{L}, E_{2}=\frac{V}{2 L}, E_{3}=\frac{2 V}{3 L} 1 / 2 \ & E_{2}<E_{3}<E_{1} \end{aligned} $$
(ii)
$$ v_{d} \propto E $$
$$ v_{d 2}<v_{d 3}<v_{d 1} $$
$$ \begin{align*} & I=n e A v_{d} \tag{iii}\ & J=n e v_{d} \end{align*} $$
$$ J_{2}<J_{3}<J_{1} $$
[CBSE Marking Scheme 2017]
