A complex current wave is given by i = 5 + 5 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The given current wave is $i = 5 + 5 \sin(100 \omega t)$.To find the average value over one time period $T$,we use the formula $\langle i \rangle

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(B) The given current wave is $i = 5 + 5 \sin(100 \omega t)$.To find the average value over one time period $T$,we use the formula $\langle i angle = \frac{1}{T} \int_{0}^{T} i \, dt$.Substituting the expression for $i$:$\langle i angle = \frac{1}{T} \int_{0}^{T} (5 + 5 \sin(100 \omega t)) \, dt$.This can be split into two parts:$\langle i angle = \frac{1}{T} \int_{0}^{T} 5 \, dt + \frac{1}{T} \int_{0}^{T} 5 \sin(100 \omega t) \, dt$.The average value of a sine function over one complete cycle is $0$,i.e.,$\langle \sin(100 \omega t) angle = 0$.Therefore,$\langle i angle = 5 + 0 = 5 	ext{ A}$.

$A$ complex current wave is given by $i = 5 + 5 \sin(100 \omega t) \text{ A}$. Its average value over one time period is given as......$\text{A}$

Similar Questions

What will be the $r.m.s.$ value of the given $A.C.$ voltage over one complete cycle?

What is the $r.m.s.$ value of an alternating current which,when passed through a resistor,produces heat that is thrice the heat produced by a direct current of $2 \ A$ in the same resistor (in $A$)?

An alternating current in a circuit is given by $I = 20 \sin (100 \pi t + 0.05 \pi) \ A$. The r.m.s. value and the frequency of the current respectively are:

The phase difference between the voltage and the current in an $AC$ circuit is $\pi / 4$. If the frequency is $50 \ Hz$,then this phase difference will be equivalent to a time of:

For an $AC$ current $I = 50 \cos(100t + 45^{\circ}) \ A$. The value of $I_{rms} =$ . . . . . . $A$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module