The rms value of AC current which when passed through a resistor produces heat energy four times that produced by DC of 2 A through the same resistor in same time, is

Question

The rms value of AC current which when passed through a resistor produces heat energy four times that produced by DC of 2 A through the same resistor in same time, is (A) 32 A (B) 2 A (C) 4 A (D) 8 A

Tardigrade Admin · Accepted Answer

Heat produce by DC H=iDC2Rt ?(i) =4Rt Heat produced by AC 4H=irms2Rt ?(ii) ∴ (4H/H)=(irms2Rt/4Rt) or irms=4A

Q. The $r m s$ value of AC current which when passed through a resistor produces heat energy four times that produced by DC of 2 A through the same resistor in same time, is

32 A

2 A

4 A

8 A

Heat produce by DC $H = i_{D C}^{2} Rt$ ?(i) $= 4 Rt$ Heat produced by AC $4 H = i_{r m s}^{2} Rt$ ?(ii) $∴$ $\frac{4 H}{H} = \frac{i _{r m s}^{2} Rt}{4 Rt}$ or $i_{r m s} = 4 A$

Q. The rms value of AC current which when passed through a resistor produces heat energy four times that produced by DC of 2 A through the same resistor in same time, is

32 A

2 A

4 A

8 A

Heat produce by DC H=iDC2​Rt ?(i) =4Rt Heat produced by AC 4H=irms2​Rt ?(ii) ∴ H4H​=4Rtirms2​Rt​ or irms​=4A

Q. The $r m s$ value of AC current which when passed through a resistor produces heat energy four times that produced by DC of 2 A through the same resistor in same time, is

Heat produce by DC $H = i_{D C}^{2} Rt$ ?(i) $= 4 Rt$ Heat produced by AC $4 H = i_{r m s}^{2} Rt$ ?(ii) $∴$ $\frac{4 H}{H} = \frac{i _{r m s}^{2} Rt}{4 Rt}$ or $i_{r m s} = 4 A$