An A.C. is given by equation I = I1 cos ω t + I2 sin ω t. The r.m.s. value of current is given by

Question

An A.C. is given by equation I = I1 cos ω t + I2 sin ω t. The r.m.s. value of current is given by (A) (I1+I2/2) (B) ((I1+I2)2/√2) (C) (1/√2)√I21+I22 (D) (I21+I22/2)

Tardigrade Admin · Accepted Answer

I=I1 cos ω t+I2 sin ω t+2I1I2 cos ω t . sin ω t I21.(1/2)I22.(1/2)+2I1I2× 0; Irms=((I21+I22)1/2/√2)

Q. An A.C. is given by equation $I = I_{1} cos ω t + I_{2} sin ω t$ . The r.m.s. value of current is given by

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

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

$\frac{1}{2} I_{1}^{2} + I_{2}^{2}$

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

$I = I_{1} cos ω t + I_{2} sin ω t + 2 I_{1} I_{2} cos ω t . sin ω t$
$I_{1}^{2} . \frac{1}{2} I_{2}^{2} . \frac{1}{2} + 2 I_{1} I_{2} \times 0; I_{r m s} = \frac{( I _{1}^{2} + I _{2}^{2} ) ^{1/2}}{2}$

Q. An A.C. is given by equation I=I1​cosωt+I2​sinωt. The r.m.s. value of current is given by

2I1​+I2​​

2​(I1​+I2​)2​

2​1​I12​+I22​​

2I12​+I22​​