An alternating current is given by I=I1 cos ω t+I2 sin ω t . The root mean square current is given by:

Question

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

Tardigrade Admin · Accepted Answer

The equation of A.C. is I=I1 cos ω t+I2 sin ω t The resultant current is given by I0=√I12+I22 Hence, the rms current from relation is I rms =(I0/√2) =(√I12+I22/√2) [ from eq. (1)] =√(I12+I22/2)

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:

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

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

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

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

The equation of A.C. is
$I = I_{1} cos ω t + I_{2} sin ω t$
The resultant current is given by
$I_{0} = I_{1}^{2} + I_{2}^{2}$
Hence, the rms current from relation is
$I_{r m s} = \frac{I _{0}}{2}$
$= \frac{I _{1}^{2} + I _{2}^{2}}{2}$ [ from eq. (1)]
$= \frac{I _{1}^{2} + I _{2}^{2}}{2}$

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​)2​

2I12​+I22​​​

2I12​+I22​​​

The equation of A.C. is I=I1​cosωt+I2​sinωt The resultant current is given by I0​=I12​+I22​​ Hence, the rms current from relation is Irms​=2​I0​​ =2​I12​+I22​​​[ from eq. (1)] =2I12​+I22​​​

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:

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

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

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

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

The equation of A.C. is
$I = I_{1} cos ω t + I_{2} sin ω t$
The resultant current is given by
$I_{0} = I_{1}^{2} + I_{2}^{2}$
Hence, the rms current from relation is
$I_{r m s} = \frac{I _{0}}{2}$
$= \frac{I _{1}^{2} + I _{2}^{2}}{2}$ [ from eq. (1)]
$= \frac{I _{1}^{2} + I _{2}^{2}}{2}$