What is the r.m.s. value of an alternating current which when passed through a resistor produces heat which is thrice of that produced by a direct current of 2 amperes in the same resistor?

Question

What is the r.m.s. value of an alternating current which when passed through a resistor produces heat which is thrice of that produced by a direct current of 2 amperes 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 ∴ i rms 2 R t=3 × i2 R t ⇒ i rms 2=3 × 22 ⇒ i rms =2 √3=3.46 A

Q. What is the r.m.s. value of an alternating current which when passed through a resistor produces heat which is thrice of that produced by a direct current of 2 amperes in the same resistor?

6 A

2 A

3.46 A

0.66 A

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

Q. What is the r.m.s. value of an alternating current which when passed through a resistor produces heat which is thrice of that produced by a direct current of 2 amperes 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 $D C$
$∴ i_{r m s}^{2} Rt = 3 \times i^{2} Rt$
$\Rightarrow i_{r m s}^{2} = 3 \times 2^{2}$
$\Rightarrow i_{r m s} = 23 = 3.46 A$