Power $P$ is to be delivered to a device via transmission cables having resistance ${R_C}$. If $V$ is the voltage across $R$ and $I$ the current through it, find the power wasted and how can it be reduced.
Cable used as transmission cable has power,
$\mathrm{P}=\mathrm{I}^{2} \mathrm{R}_{\mathrm{C}}$
$\mathrm{R}_{\mathrm{C}}=$ resistance of cable
$\mathrm{P}=\mathrm{VI}$
Given power can be transmitted in two different ways.
$(1)$ Low voltage and high current
$(2)$ High voltage and low current
At low voltage and high current power transmitted according to $\mathrm{P} \propto \mathrm{I}^{2}$ will be higher.
Thus, when transmission is done at higher voltage dissipation (wastage) will be less.
A steady current $I$ flows through a wire of radius $r$, length $L$ and resistivity $\rho$. The current produces heat in the wire. The rate of heat loss in a wire is proportional to its surface area. The steady temperature of the wire is independent of
Assertion : Long distance power transmission is done at high voltage.
Reason : At high voltage supply power losses are less.
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For driving a current of $2\, A$ for $6$ minutes in a circuit, $1000\, J$ of work is to be done. The $e.m.f.$ of the source in the circuit is ................ $V$
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