In an electric circuit, two resistors of resistance R and 2R are connected in series. The ratio of the thermal energy developed in R to that in 2R is

Step-by-step solution

In a series circuit, the current I flowing through all the resistors is the same. The thermal energy developed in a resistor of resistance R over a time t is given by Joule's law of heating: H = I^2 R t For the first resistor of resistance R , the thermal energy developed is: H₁ = I^2 R t For the second resistor of resistance 2R , the thermal energy developed is: H₂ = I^2 (2R) t The ratio of the thermal energy developed in R to that in 2R is: H₁ H₂ = I^2 R t I^2 (2R) t = 1 2 Thus, the ratio is 1 : 2 .