Question

Two resistors equal resisitances 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 amount 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: (A), (D)

equal amounts of thermal energy must be produced in the resistors
the temperature may rise equally in the resistors

Let, $R_1$ and $R_2$ be the resistances of the two resistors, $R_1=R_2$. Also, $I_1$ and $I_2$ be the current flowing through resistors $R_1$ and $R_2$ respectively. Since the resistors are connected in series $I_1=I_2$.
According to Joule's law of heating, at constant temperature heat produced in resistors $R_1$ and $R_2$ in time t, is
$Q_1=I_1^2{R}_{1}t$ and $Q_2=I_2^2{R}_{2}t$
Since, $R_1=R_2$ and $I_1=I_2$ $\Rightarrow Q_1=Q_2$
Hence, equal heat is produced in two resistors.
Also, neglecting the variation in resistances of resistors with temperature, $R_1=R_2=constant$. Hence, the heats produced are
$Q_1\propto I_1^2$ and $Q_2\propto I_2^2$
Hence, depending on rise in current through resistors, the temperature may rise equally in the resistors.