Question

A direct of current of $2A$ and an alternating current having a maximum value of $2A$ flow through two identical resistance. The ratio of heat produced in the two resistances in the same time interval will be:

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $4:1$

Answer 1

Answer: (A), (C)

The correct options are
A $1:1$
C $2:1$

The rms value of the current is given as,

$I_{rms}=\frac{I_0}{\sqrt{2}}$

The ratio of heat produced in the two resistance is given as,

$r=\frac{I^{2}Rt}{{I^2}_{rms}Rt}$

$=\frac{{\left(2\right)}^2}{{\left(\frac{2}{\sqrt{2}}\right)}^2}$

$=\frac{2}{1}$

Thus, the ratio of heat produced in the two resistances in the same interval will be $\frac{2}{1}$.