An alternating current is given by I = I 1 cos ω t +I2 sin ω t, the root mean square current is given by

Question

An alternating current is given by I = I 1 cos ω t +I2 sin ω t, the root mean square current is given by (A) (I1+I2/√2) (B) (|I1+I2|/2) (C) √(I12+I22/2) (D) (√I12+I22/2)

Tardigrade Admin · Accepted Answer

The equation of alternating current (AC) is given by I=I1 cos ω t+I2 sin ω t The resultant current I0=√I1 2+I2 2 Also, rms value of current is given by I rms =(I0/√2) ⇒ I rms =√(I1 2+I2 2/2)

Q. An alternating current is given by $I = I_{1} cos ω t + I_{2} sin ω t$ , the root mean square current is given by

$\frac{I _{1} + I _{2}}{2}$

$\frac{∣ I _{1} + I _{2} ∣}{2}$

$\frac{I _{1}^{2} + I _{2}^{2}}{2}$

$\frac{I _{1}^{2} + I _{2}^{2}}{2}$

The equation of alternating current (AC) is given by
$I = I_{1} cos ω t + I_{2} sin ω t$
The resultant current
$I_{0} = I_{1}^{2} + I_{2}^{2}$
Also, $r m s$ value of current is given by
$I_{r m s} = \frac{I _{0}}{2}$
$\Rightarrow I_{r m s} = \frac{I _{1} ^{2} + I _{2} ^{2}}{2}$

Q. An alternating current is given by I=I1​cosωt+I2​sinωt, the root mean square current is given by

2​I1​+I2​​

2∣I1​+I2​∣​

2I12​+I22​​​

2I12​+I22​​​

The equation of alternating current (AC) is given by I=I1​cosωt+I2​sinωt The resultant current I0​=I1​2+I2​2​ Also, rms value of current is given by Irms​=2​I0​​ ⇒Irms​=2I1​2+I2​2​​

Q. An alternating current is given by $I = I_{1} cos ω t + I_{2} sin ω t$ , the root mean square current is given by

$\frac{I _{1} + I _{2}}{2}$

$\frac{∣ I _{1} + I _{2} ∣}{2}$

$\frac{I _{1}^{2} + I _{2}^{2}}{2}$

$\frac{I _{1}^{2} + I _{2}^{2}}{2}$

The equation of alternating current (AC) is given by
$I = I_{1} cos ω t + I_{2} sin ω t$
The resultant current
$I_{0} = I_{1}^{2} + I_{2}^{2}$
Also, $r m s$ value of current is given by
$I_{r m s} = \frac{I _{0}}{2}$
$\Rightarrow I_{r m s} = \frac{I _{1} ^{2} + I _{2} ^{2}}{2}$