Question 208: Current Electricity

Question

An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14 $$\Omega$$. If this single copper wire of the cable is replaced by seven identical well insulated copper wires each of radius 3 mm connected in parallel, then the new resistance of the combination will be :

Accepted Answer

Initially, copper wire radius (r
1
) = 9 mm
Resistance (R) = 14 $$\Omega$$
We know, $$R = {{ho L} \over A} = {{ho L} \over {\pi r_1^2}} = 14$$
Now this copper wire is replaced by 7 parallel copper wire of resistance R
1
.
$$	herefore$$ Equivalent resistance of 7 parallel copper wire,
$${1 \over {{R_{eq}}}} = {1 \over {{R_1}}} + {1 \over {{R_1}}} + {1 \over {{R_1}}} + {1 \over {{R_1}}} + {1 \over {{R_1}}} + {1 \over {{R_1}}} + {1 \over {{R_1}}}$$
$$ \Rightarrow {1 \over {{R_{eq}}}} = {7 \over {{R_1}}}$$
$$ \Rightarrow {R_{eq}} = {{{R_1}} \over 7}$$
$$ = {1 \over 7} 	imes {{ho L} \over {\pi r_2^2}}$$
$$ = {1 \over 7} 	imes {{ho L} \over {\pi {{\left( {{{{r_1}} \over 3}} ight)}^2}}}$$ [as $${r_2} = {{{r_1}} \over 3}$$ ; $${r_1} = 9$$ m and $${r_2} = 3$$]
$$ = {1 \over 7} 	imes {{ho L} \over {\pi r_1^2}} 	imes 9$$
$$ = {1 \over 7} 	imes 14 	imes 9$$
$$ = 18\,\Omega $$

Answer

9 $$\Omega$$

Answer

18 $$\Omega$$

Answer

28 $$\Omega$$

Answer

126 $$\Omega$$

Current Electricity

An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14 $\Omega$. If this single copper wire of the cable is replaced by seven identical well insulated copper wires each of radius 3 mm connected in parallel, then the new resistance of the combination will be :

Choose the correct answer: