RMS Value of Current in Sinusoidal AC

Q. If an alternating voltage is represented as E = 141 sin (628 t), then the rms value of the voltage and the frequency are respectively

1. 141 V, 628 Hz
2. 100 V, 50 Hz
3. 100 V, 100 Hz
4. 141 V, 100 Hz

Q. A small circular loop of radius $l=1cm$ is kept inside a larger circular loop of radius r such that both are coplanar and concentric. If the current in larger loop is as shown in the graph, then current induced in the smaller loop any time is represented as $I_n$ at any instant. Take anticlockwise current as positive. List -1 contains time instants, and List-2 contains the values for $I_n$. Match them. Take $\frac{{\mu }_0\pi }{2Rr}=1$.

$\begin{array}{cccc}& \text{List -1}& & \text{List -2}\\ \left(I\right)& 0sec& \left(p\right)& 25\mu A\\ \left(II\right)& \frac{1}{3}sec& \left(Q\right)& 12.5\mu A\\ \left(III\right)& \frac{3}{2}sec& \left(R\right)& 0\mu A\\ \left(IV\right)& \frac{5}{3}sec& \left(S\right)& -6.25\mu A\\ & & \left(T\right)& -12.5\mu A\\ & & \left(U\right)& -25\mu A\end{array}$

1. $I\to P,II\to R,III\to U,IV\to P$
2. $I\to U,II\to R,III\to P,IV\to U$
3. $I\to P,II\to R,III\to P,IV\to P$
4. $I\to U,II\to R,III\to U,IV\to U$

Q. The self inductance of a closed-packed coil is $8\text{mH}$. A current of $5\text{mA}$ is passed through it. Find the magnetic flux per unit turn of the coil, if it has $100$ turns.

Q. Find the average value of current (in A) as shown graphically in the figure, from $t=0$ to $t=2s$.

Q. In a certain circuit current changes with time according to $i=2\sqrt{t}$.The r.m.s value of current between t = 2 to t = 4s will be

1. $3A$
2. $3\sqrt{3}A$
3. $2\sqrt{3}A$
4. $(2-\sqrt{2})A$

Q. Determine the rms value of a semi-circular current wave which has a maximum value of a Ampere. The y axis denotes current in Ampere and x axis denotes time.

1. $\left(\frac{1}{\sqrt{2}}\right)a$
2. $\sqrt{\frac{3}{2}}a$
3. $\sqrt{\frac{2}{3}}a$
4. $\sqrt{\frac{1}{3}}a$