Which heater will perish under the test?

Question:

2 heaters with rating of !!10W!! at !!200V!! and !!20W!! at !!100V!! are connected in series. If they are connected to !!300V!! supply then:

  • !!10W!! heater may burn

  • !!20W!! heater may burn

  • Both of them will burn

  • None of them will burn

Solution

This was a straighforward question.

We first use the information given to find the resistance of the 2 capacitors.

!!R_1=(200)^2/10!!

!!R_2=(100)^2/20!!

When combined in a series to a !!300V!! power source, current through circuit is !!=300/((200)^2/10+(100)^2/20)!!

!!=3/(40+5)=1/15A!!

Heat generated in each of the heaters is given by !!I^2R!!.

Heat in first is !!I^2R_1=(1/15)^2xx(200)^2/10=(8xx20)/9>10W!!

Heat in first is !!I^2R_1=(1/15)^2xx(100)^2/20=(4*5)/9<20W!!

So the first heater burns.

Alternatively:

We can see that the maximum current that can pass through first heater is !!P/V=1/20A!! similarly the maximum current through second resistor is !!P/V=1/5A!!

Since the current through both the heaters is !!1/15A!! first heater burns.

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