Question

A direct current of $2A$ and an alternating current having a maximum value of $2A$ flow through two identical resistances. 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

The correct option is C $2:1$

Heat produced due to DC current $=I^{2}RT$

Heat produced due to AC current $=I_{rms}^{2}RT$

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

$\therefore$ Ration of heat produced in two resistance

$=\frac{H_{DC}}{H_{AC}}$

$=\frac{I^{2}RT}{{\left(\frac{I_0}{\sqrt{2}}\right)}^{2}RT}$

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

$=\frac{2}{1}$