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

Option: 1

3:2


Option: 2

3:1


Option: 3

3:4


Option: 4

4:3


Answers (1)

best_answer

\mathrm{ I_{D C}=4 A \\ }

\mathrm{ T_0=4 A \\ }

\mathrm{ R_1=3 \Omega \\ }

\mathrm{ R_2=2 \Omega }
Let the ratio of heat produced in the two resistance in same interval of time be \mathrm{\mathrm{H}_1 \& \mathrm{H}_2} respectively.

\mathrm{\frac{H_{1}}{H_{2}}=\frac{I^{2}_{DC}R_{1}\left ( \Delta t \right )}{I^{2}_{rms}R_{2}\Delta t}=\frac{16\times 3}{\left ( \frac{4}{\sqrt{2}} \right )^{2}\times 2}}

\mathrm{\frac{H_{1}}{H_{2}}=3}

Hence 2 is correct option.

Posted by

vinayak

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