Question

Two resistors of equal resistances are joined in series and a current is passed through the combination. Neglect any variation in resistance as the temperature changes. In a given time interval,
(a) equal amounts of thermal energy must be produced in the resistors
(b) unequal amounts of thermal energy may be produced
(c) the temperature must rise equally in the resistors
(d) the temperature may rise equally in the resistors

Answer 1

Answer:THE CORRECT ANSWERS ARE (A) AND (D)

Explanation: LET US CONSIDER THAT THE CURRENT "i" IS FLOWING THROUGH THE COMBINATION FOR "t" SECONDS

Since equal amount of current flows through the resistors as they are connected in series

H₁=i²rt

H₂=i²rt

in both the cases "i" is  same, because they are connected in series, "R" is same as it is given, and time "t" is also same

therefore equal amounts of thermal energy must be produced in the resistors

we know that temperature is directly proportional to the energy or heat  produced

energy is directly proportional to the resistances

H∝R

H∝R₀+αt

this α changes for every metal, therefore temperature raised may be equal or not

hence options A and D are correct  

Answer 2

(a) In the resistors, equal amounts of thermal energy should be produced.

(b) In the resistors, the temperature may  equally rise.

Explanation:

• The resistor with resistance R has the current i passing through it for time t. Then, the produced thermal energy will be shown as  $H=i^{2} R t$
• The current passing through the resistors will be the same. So, in a resistor, the amount of produced thermal energy is the same.
• The size and shape of the resistor has an impact on the temperature rise.