A direct current of 4 A and an alternating current of peak value 4 A flow through resistance of 3Ω and 2Ω respectively. The ratio of heat produced in the two resistances in same interval of time will

Question

A direct current of 4 A and an alternating current of peak value 4 A flow through resistance of 3Ω and 2Ω respectively. The ratio of heat produced in the two resistances in same interval of time will be :

TestHub · Accepted Answer

Heat produced in resistor when direct current flows is $H_{1} = i^{2} R_{1} t$
$H_{1} = 4^{2} (3) t = 16 (3) t$
Heat produced in resistor when alternating current flows is $H_{2} = i_{r m s}^{2} R_{2} t {i_{r m s} = \frac{i _{0}}{2}}$
$H_{2} = \frac{i _{0}^{2}}{2} R_{2} t$
$H_{2} = \frac{4 ^{2}}{2} \times (2) t = 16 t$
Thus, the ratio is $H_{1} : H_{2} = 3 : 1$

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