An alternating current is given by the equation i = i 1 sin ω t + i 2 cos ω t The rms current will be

Question

An alternating current is given by the equation i = i 1 sin ω t + i 2 cos ω t The rms current will be (A) (1/√2)(i12+i22)(1/2) (B) (1/√2)( i 1+ i 2)2 (C) (1/2)(i12+i22)(1/2) (D) (1/√2)( i 1+ i 2)

Tardigrade Admin · Accepted Answer

i = i 1 sin ω t + i 2 sin (ω t +90) i =√ i 12+ i 22 sin (ω t +φ) i rms =( i 0/√2)=(√ i 12+ i 22/√2)

Q. An alternating current is given by the equation $i = i_{1} sin ω t + i_{2}$ cos $ω t$ The rms current will be

$\frac{1}{2} (i_{1}^{2} + i_{2}^{2})^{\frac{1}{2}}$

$\frac{1}{2} (i_{1} + i_{2})^{2}$

$\frac{1}{2} (i_{1}^{2} + i_{2}^{2})^{\frac{1}{2}}$

$\frac{1}{2} (i_{1} + i_{2})$

$i = i_{1} sin ω t + i_{2} sin (ω t + 90)$
$i = i_{1}^{2} + i_{2}^{2} sin (ω t + ϕ)$
$i_{r m s} = \frac{i _{0}}{2} = \frac{i _{1}^{2} + i _{2}^{2}}{2}$

Q. An alternating current is given by the equation i=i1​sinωt+i2​ cos ωt The rms current will be

2​1​(i12​+i22​)21​

2​1​(i1​+i2​)2

21​(i12​+i22​)21​

2​1​(i1​+i2​)

i=i1​sinωt+i2​sin(ωt+90) i=i12​+i22​​sin(ωt+ϕ) irms​=2​i0​​=2​i12​+i22​​​

Q. An alternating current is given by the equation $i = i_{1} sin ω t + i_{2}$ cos $ω t$ The rms current will be

$\frac{1}{2} (i_{1}^{2} + i_{2}^{2})^{\frac{1}{2}}$

$\frac{1}{2} (i_{1} + i_{2})^{2}$

$\frac{1}{2} (i_{1}^{2} + i_{2}^{2})^{\frac{1}{2}}$

$\frac{1}{2} (i_{1} + i_{2})$

$i = i_{1} sin ω t + i_{2} sin (ω t + 90)$
$i = i_{1}^{2} + i_{2}^{2} sin (ω t + ϕ)$
$i_{r m s} = \frac{i _{0}}{2} = \frac{i _{1}^{2} + i _{2}^{2}}{2}$