The rate of heat produced in a resistor is given by ( P = I^2R ), where ( P ) is the power, ( I ) is the current, and ( R ) is the resistance.
Correct answer: A. 2 A
- A. 2 A
- B. ( sqrt{2} ) A
- C. 1 A
- D. ( 2sqrt{2} ) A
Explanation
For the alternating current (r.m.s) and the direct current to produce heat at the same rate in identical resistors, their powers must be equal:[ I_{{rms}}^2 R = I^2 R ]Given that ( I_{{rms}} = 2 , {A} ), we can solve for ( I ):[ (2 , {A})^2 R = I^2 R ][ 4R = I^2 R ][ I^2 = 4 ][ I = 2 ]So, the current ( I ) for the steady direct current is 2 A.Now, let's compare this with the provided options:
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