Question

two electric bulbs are rated as 2KW-10A & 240V-120W. What is the ratio of produced heat when they are connected in parallel and series with 200V?

Answer 1

First we make an assumption that the resistance of the bulbs will be the rated resistance when operated at their rated power and voltage. (this is sometimes not the case as resistance can vary with temperature and temperature can vary with power).
Step 1. Calculate the resistance of each bulb.. The 2 Kw bulb: Use P = I^2 R,
2000=10^2 R, 2000 = 100 R
R=2000/100 = 20 Ohms

The other bulb. P = E^2/R = (240 X 240)/R or 120W= 57600/R
R = 57600/120 = 480 Ohm

Step 2. Calculate the power dissipated when the voltage is 200 Volts.
P = E^2/R, P = 40000/R

Calculate power for both conditions. Series- R= 480 + 20 = 500
P = 40000/500 = 80 watts.
Parallel, R = (480 X 20)/(480 + 20)= 19.2 Ohm, P=40000/19.2 = 2083.3333

Make the assumption that the power is all converted to heat.
Now calculate the ratio 2083.3333/80 approx 26 to 1

Answer 2

thank you :)