What is the (rms) value of an alternating current which when passed through a resistor produces heat which is thrice that of produced by a direct current of 2 A in the same resistor?

Question

What is the (rms) value of an alternating current which when passed through a resistor produces heat which is thrice that of produced by a direct current of 2 A in the same resistor? (A) 6 A (B) 2 A (C) 3.46 A (D) 0.66 A

Tardigrade Admin · Accepted Answer

Heat produced by AC=3 × Heat produced by DC ∴ irms2Rt=3× i2Rt ⇒ irms2=3× 22 irms=2√3=3.46A

Q. What is the (rms) value of an alternating current which when passed through a resistor produces heat which is thrice that of produced by a direct current of 2 A in the same resistor?

6 A

2 A

3.46 A

0.66 A

Heat produced by $A C = 3 \times$ Heat produced by $D C$ $∴$ $i_{r m s}^{2} Rt = 3 \times i^{2} Rt$ $\Rightarrow$ $i_{r m s}^{2} = 3 \times 2^{2}$ $i_{r m s} = 23 = 3.46 A$

Q. What is the (rms) value of an alternating current which when passed through a resistor produces heat which is thrice that of produced by a direct current of 2 A in the same resistor?

6 A

2 A

3.46 A

0.66 A

Heat produced by AC=3× Heat produced by DC ∴ irms2​Rt=3×i2Rt ⇒ irms2​=3×22 irms​=23​=3.46A

Heat produced by $A C = 3 \times$ Heat produced by $D C$ $∴$ $i_{r m s}^{2} Rt = 3 \times i^{2} Rt$ $\Rightarrow$ $i_{r m s}^{2} = 3 \times 2^{2}$ $i_{r m s} = 23 = 3.46 A$