What is the rms value of an alternating current which when passed through a resistor produces heat, which is thrice that produced by a current of $2$ ampere in the same resistor in the same time interval?

6

ampere

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2

ampere

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2 \sqrt{3}

ampere

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0.65

ampere

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Solution

The correct option is C $2 \sqrt{3}$ ampere
We know heat produced by a resistor is
H=iRt
where t=time interval
$H_{1} = i_{1}^{2} R t = 2^{2} R t = 4 R t H_{2} = I_{2}^{2} R t g i v e n t h a t H_{2} = 3 H_{1} I_{2}^{2} R t = 3 \times 4 R t I_{2}^{2} = 12 I_{2} = \sqrt{12} = 2 \sqrt{3}$

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What is the rms value of an alternating current which when passed through a resistor produces heat, which is thrice that produced by a current of 2 ampere in the same resistor in the same time interval?

The correct option is C 2√3 ampereWe know heat produced by a resistor is H=iRtwhere t=time intervalH1=i21Rt=22Rt=4RtH2=I22RtgiventhatH2=3H1I22Rt=3×4RtI22=12I2=√12=2√3

What is the rms value of an alternating current which when passed through a resistor produces heat, which is thrice that produced by a current of $2$ ampere in the same resistor in the same time interval?

The correct option is C $2 \sqrt{3}$ ampere
We know heat produced by a resistor is
H=iRt
where t=time interval
$H_{1} = i_{1}^{2} R t = 2^{2} R t = 4 R t H_{2} = I_{2}^{2} R t g i v e n t h a t H_{2} = 3 H_{1} I_{2}^{2} R t = 3 \times 4 R t I_{2}^{2} = 12 I_{2} = \sqrt{12} = 2 \sqrt{3}$