Eight copper wire of length $l$ and diameter $d$ are joined in parallel to form a single composite conductor of resistance $R$. If a single copper wire of length $2\,l$ have the same resistance $(R)$ then its diameter will be $.....d$.
A$3$
B$4$
C$2$
D$1$
JEE MAIN 2022, Easy
Download our app for free and get started
B$4$
b Each wire has resistance $=\rho \frac{4 \ell}{\pi d ^{2}}=r$
Eight wire in parallel, then equivalent resistance is $\frac{ r }{8}=\frac{\rho \ell}{2 \pi d ^{2}}$
Single copper wire of length $2 l$ has resistance
$R =\rho \frac{2 \ell \times 4}{\pi d _{1}^{2}}=\frac{\rho \ell}{2 \pi d ^{2}}$
$d _{1}=4 d$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Water of volume $2\, litre$ in a container is heated with a coil of $1\, kW$ at $27 \,^oC$. The lid of the container is open and energy dissipates at rate of $160\, J/s$. In how much time temperature will rise from $27\,^oC$ to $77\,^oC$ $[$ Given specific heat of water is $4.2\, kJ/kg$ $]$
The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of $15\, \Omega$ resistance is connected across $BD$. Calculate the current through the galvanometer when a potential difference of $10\, V$ is maintained across $AC.$
$n$ identical cells each of $e.m.f.$ $E$ and internal resistance $r$ are connected in series. An external resistance $R$ is connected in series to this combination. The current through $R$ is
First, a set of ${n}$ equal resistors of $10\; \Omega$ each are connected in series to a battery of emf $20\; {V}$ and internal resistance $10\; \Omega .$ A current $I$ is observed to flow. Then, the $n$ resistors are connected in parallel to the same battery. It is observed that the current is increased $20$ times, then the value of $n$ is .... .
When a piece of aluminium wire of finite length is drawn through a series of dies to reduce its diameter to half its original value, its resistance will become ........ times