Two electric lamps are rated as 220V. 40 W and 220V,60W. Find the heat generated per second in lamp when they are connected in series across 220V mains. Given 1 cal=4.2J.

Explanation

For the first lamp
`P_(1) = 60 ` watts
`V_(1) = 220 ` volts
`P_(1) = V_(1)I_(1) = (V_(1)^(2))/(R_(1))`
` or R_(1) = (V_(1)^(2))/(P_(1))`
`R_(1) = ((220)^(2))/(60)= (48400)/(60) ohm = 806.7 ohm`
For the second lamp
`P_(2) = 40` watt
`V_(2) = 220` volt
`P_(2) = V_(2)l_(2) = (V_(2)^(2))/(R_(2))`
` R_(2) = (V_(2)^(2))/(P_(2)) = ((220)^(2))/(40) = 1210` ohms
When electric lamps are joined in series,
`R = R_(1) + R_(2) = 806.7 + 1210 = 2016.7 Omega`
`therefore ` l = current through each bulb `= (V)/(R) = (220)/(2016.7) A`
` therefore ` `H_(1)` = heat produced per second in first bulb ` = l_(2)R_(1) = ((220)/(2016.7))^(2) xx806.7 = 9.60 Js^(-1)`
`therefore ` `H_(2)` = heat produced per second in second bulb ` = I^(2)R_(2) = ((220)/(2016.7))^(2) xx 1210 = 14.4 Js^(-1)`