State joule's law. An electric iron consumes energy at rate of 420w when heating is at maximum rate and 180 w when heating Is at minimum. The voltage is 220V .What is the current and resistant in each case?

Explanation

Joules Law states that the heat produced in the conductor is always directly proportional to:
(i) the square of the current flowing through the conductor.
(ii) resistance of the conductor.
(iii) time for which the current flows through the conductor.
Deriving Joules Law
Potential difference V = Work done W/ Charge moved Q
V=W/Q
`W=VxxQ`....(1)
Now
P=W/t
`P=VxxQ//t` ..... from 1
`P=VxxI` ......... since Current I=Q/t ........2
Now,
`P=Wxxt`
`W=Pxxt`
`W=VIxxt`
By ohm.s law
`V=IxxR`
therefore ,
`W=IxxR xx I xxt`
`W=I^2 xx R xxt`
But as all the work done to move unit charge offered resistance gets converted into heat energy
`H=I^2 xx R xxt`
Now 1) In the first case
Energy rating means Power
Now Power = 420 W
Potential difference =220 V
Now
P=V x I
I=P/V = 420/220 = 21/11
I=21/11 Amperes
Now , `V=I xx R , 220 = 21/11 xx R`
Or, `R=220xx11//21` ohms
(2) In the second case
Power = 180 W
potential difference =220 V
`P=VxxI`
`I=P//V`
180 = 220/I
I=180/220
I=9/11 Amperes
Now,
`V=IxxR`
`220=9//11xxR`
`R=269Omega` ohms.