Question

An electric geyser consumes energy at a rate of $1000$watt, when the heating is at the minimum rate. And $500$ watt, when the heating is at the minimum rate. The voltage is $220$volt, what are the values of the current and the resistance in each case?

Answer 1

Hint: Joules law of heating is heat generated in a considered ids directly proportional to voltage given and in directly proportional to current passing through conduct with respect to time. Due to the willingness of electrons in the wire of resistance energy is lost, easing the heating of the resistor. In simple current heat is generated due to work done by the charges moving in circuit.

Complete step by step answer:
Power = $VI = \dfrac{{{v^2}}}{R}$
When v is voltage, I is current, R is resistance.
First case,
Power= $1000w \Rightarrow 1000 = 220 \times I$
$ \Rightarrow I = 4.54A$
$ \Rightarrow 1000 = \dfrac{{{{220}^2}}}{R}$
$R = \dfrac{{{{220}^2}}}{{1000}}$
$ = \dfrac{{220 \times 220}}{{1000}}$
$ = \dfrac{{22 \times 22}}{{10}}$
$ = 48.4\Omega $
Second Case,
Power$ = 500w = 220 \times I$
$ \Rightarrow I = 2.27A$
$ \Rightarrow 500 = \dfrac{{{{220}^2}}}{R}$$ \Rightarrow 500 = \dfrac{{{{220}^2}}}{R}$
$R = \dfrac{{220 \times 220}}{{500}}$
$R = \dfrac{{22 \times 22}}{5}$
$R = 96.8\Omega $
The value of current when energy current at rate of $1000$watt is $4.54A$ and resistance is $48.4\Omega $

The value of current when energy current at a rate of $500$watt is $2.27A$ and resistance is $96.8\Omega $.

Note:
The heat dissipated in circuit is directly proportional to square of current flowing energy and also proportional to resistance of circuit. Higher the amount of current in circuit higher is the amount of heat generated. An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge past a region. A current always flows from higher potential to lower potential. SI unit of current is Ampere.