RMS Value of Current in Sinusoidal AC

Q. In the below figure, a square loop consisting of an inductor of inductance L and resistor of resistance R is placed between two long parallel wires. The two long straight wires have time-varying current of magnitude $I=I_{0}cos\omega t$ A but the directions of current in them are opposite.

Total magnetic flux in this loop is

1. $\frac{{\mu }_{0}a{I}_{0}cos\omega t}{\pi }ln2$
2. $\frac{2{\mu }_{0}a{I}_{0}cos\omega t}{\pi }ln2$
3. $\frac{4{\mu }_{0}a{I}_{0}cos\omega t}{\pi }ln2$
4. $\frac{{\mu }_{0}a{I}_{0}cos\omega t}{2\pi }ln2$

Q. In the below figure, a square loop consisting of an inductor of inductance L and resistor of resistance R is placed between two long parallel wires. The two long straight wires have time-varying current of magnitude $I=I_{0}cos\omega t$ $A$, but the directions of current in them are opposite.Magnitude of emf in this circuit only due to flux change associated with two long straight current carrying wires will be

1. $\frac{{\mu }_{0}aln2I_0\omega }{\pi }sin\omega t$
2. $\frac{2{\mu }_{0}aln2I_0\omega }{\pi }sin\omega t$
3. $\frac{{\mu }_{0}aln2I_0\omega }{2\pi }cos\omega t$
4. $\frac{{\mu }_{0}aln2I_0\omega }{\pi }cos\omega t$

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. $\sqrt{\frac{1}{3}}a$

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. 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. $(2-\sqrt{2})A$