Question

If a 120-volt, 50 watt lamp is connected in series with a 120-volt, 75-watt lamp, and the series circuit is supplied with a 240-volt source, the lamps will operate at their rated power outputs.True / False.

Answer 1

Answer:False

Step-by-step explanation:

Given

Power of first lamp
`P=50\ W` at
`V=120\ V`

Power of second lamp
`P=75\ W` at
`V=120\ V`

Resistance of two lamps is given by

`R=(V^2)/(P)`

`R_1=(120^2)/(50)`

`R_1=288\ \Omega`

For
`R_2=(120^2)/(75)`

`R_2=192\ \Omega`

If both the lamps are connected in series with 240 V source then the current in the circuit is

`i=(V)/(R)`

`i=(240)/(192+288)`

`i=0.5\ A`

Power of first lamp
`P_1=i^2R_1`

`P_1=(0.5)^2* 288`

`P_1=72\ W`

`P_2=(0.5)^2* 192`

`P_2=48\ W`

Thus both operate at lower range of rated power