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.