AC Basics: Peak, RMS & Average Values

An alternating voltage is given by $V = V_0 \sin\left(\omega t + \frac{\pi}{4}\right)$. The time when the voltage is maximum for the first time is

($T$ = periodic time of the alternating voltage, $\cos 0^\circ = \sin 90^\circ = 1$)

An AC source is $120$ V - $60$ Hz. The value of voltage after $\frac{1}{720}$ s from start will be $\left(\sin 30^\circ = \frac{1}{2}\right)$

An alternating voltage is $E = 100 \sin\left(\omega t + \frac{\pi}{6}\right)$ V. The voltage will be maximum for the first time when t is

$\left(\sin \frac{\pi}{2} = 1\right)$ (T = Periodic time)

The peak value of an alternating current is 5 A and frequency is 60 Hz. How long will the current, starting from zero, take to reach the peak value?

A resistance of $20\ \Omega$ is connected to a source of alternating potential $V = 220 \sin(100\pi t)$. The time taken by current to change from its peak value to r.m.s. value is $\left(\sin \frac{\pi}{4} = \frac{1}{\sqrt{2}}\right)$

An alternating e.m.f. is given by $e = e_0 \sin \omega t$. In what time the e.m.f. will have half its maximum value, if 'e' Starts from zero?

An alternating e.m.f. is given by $e = e_0 \sin \omega t$. In what time the e.m.f. will have half its maximum value, if 'e' starts from zero? ($\sin 30^\circ = 0.5$)

The electric current in the circuit is given as $i = i_o (t/T)$. The r.m.s current for the period $t = 0$ to $t = T$ is ______.

The instantaneous value of current in an a.c. circuit is $I = 3 \sin\left(50\pi t + \frac{\pi}{4}\right)\text{ A}$. The current will be maximum for the first time at

An ac current is represented as

$i = 5\sqrt{2} + 10 \cos\left(650\pi t + \frac{\pi}{6}\right)\text{ Amp}$

The r.m.s value of the current is

An alternating current is represented by the equation, $i = 100\sqrt{2} \sin(100\pi t)$ ampere. The RMS value of current and the frequency of the given alternating current are

An electric bulb rated as $100\text{ W} - 220\text{ V}$ is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is:

An alternating current is given by $I = I_A \sin \omega t + I_B \cos \omega t$. The r.m.s current will be

An alternating e.m.f. is given by $e = e_0 \sin \omega t$. In how much time the e.m.f. will have half its maximum value, if e starts from zero?

$(T =$ Time Period, $\sin 30^\circ = \frac{1}{2})$

The alternating voltage is given by $v = v_0 \sin\left(\omega t + \frac{\pi}{3}\right)$ when will be the voltage maximum for first time?

An alternating current is given by $I = 100 \sin(50\pi t)$. How many times will the current become zero in one second?

In an a.c. circuit $I = 100 \sin 200\pi t$. The time required for the current to achieve its peak value will be

An alternating current at any instant is given by $i = [6 + \sqrt{56} \sin(100\pi t + \pi/3)]$ A. The rms value of the current is ______ A.

An alternating voltage $V(t) = 220 \sin 100\pi t$ volt is applied to a purely resistive load of $50\ \Omega$. The time taken for the current to rise from half of the peak value to the peak value is:

A group of lamps having total power rating of $1000\text{ W}$ is supplied by an AC voltage of $E = 200 \sin(310t + 60^\circ)$, the rms value of current flowing through the circuit is

The a.c. source of e.m.f. with instantaneous value '$e$' is given by $e = 200 \sin(50t)$ volt. The r.m.s. value of current in a circuit of resistance $50\ \Omega$ is

The current flowing through an ac circuit is given by

I = 5 sin(120$\pi$t)A

How long will the current take to reach the peak value starting from zero?

A standard filament lamp consumes 100 W when connected to 200 V ac mains supply. The peak current through the bulb will be:

The peak voltage of the ac source is equal to

A direct current of $4\text{ A}$ and an alternating current of peak value $4\text{ A}$ flow through resistance of $3\ \Omega$ and $2\ \Omega$ respectively. The ratio of heat produced in the two resistances in same interval of time will be:

In a full wave rectifier circuit without filter, the output current is

A resistance of 40 $\Omega$ is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by the current to change from its maximum value to the rms value:

A 220 V, 50 Hz AC source is connected to a 25 V, 5 W lamp and an additional resistance R in series (as shown in figure) to run the lamp at its peak brightness, then the value of R (in ohm) will be _____________.

The peak value of an alternating emf '$e$' given by $e = e_0 \cos \omega t$ is 10 volt and its frequency is $50\text{ Hz}$. At time $t = \frac{1}{600}\text{ s}$, the instantaneous e.m.f is $\left(\cos \frac{\pi}{6} = \sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}\right)$

An alternating voltge is represented by $V = 80 \sin(100\pi t) \cos(100\pi t)$ volt. The peak voltage is

An AC source rated 220 V, 50 Hz is connected to a resistor. The time taken by the current to change from its maximum to the rms value is:

An alternating e.m.f. is $e = e_0 \sin \omega t$. In what time the e.m.f. will have half its maximum value, if '$e$' starts from zero? ($T =$ time period, $\sin 30^\circ = 0.5$)

The instantaneous value of an alternating current is given by $i = 50 \sin(100\pi t)$. It will achieve a value of $25\text{ A}$ after a time interval of $(\sin 30^\circ = 0.5)$

A 10 $\Omega$ resistance is connected across 220V $-$ 50 Hz AC supply. The time taken by the current to change from its maximum value to the rms value is:

An AC current is given by I = I1 sin$\omega$t + I2 cos$\omega$t. A hot wire ammeter will give a reading:

An alternating current is given by the equation i = i1 sin $\omega$t + i2 cos $\omega$t. The rms current will be:

The alternating current is given by $i = \left\{\sqrt{42} \sin\left(\frac{2\pi}{T} t\right) + 10\right\} A$

The r.m.s. value of of this current is ................. A.

An alternating voltage is given by $E = 100 \sin\left(\omega t + \frac{\pi}{6}\right)\text{ V}$. The voltage will be maximum for the first time when is [ $T =$ periodic time)

The variation of EMF with time for four types of generators are shown in the figures. Which amongst them can be called AC?

An alternating voltage v(t) = 220 sin 100 $\pi$t volt is applied to a purely resistance load of 50$\Omega$. The time taken for the current to rise from half of the peak value to the peak value is:

The AC voltage across a resistance can be measured using a:

The r.m.s. value of potential difference V shown in the figure is

Alternating current can not be measured by $\text{D.C.}$ ammeter because

In an A.C. circuit, $I_{\text{rms}}$ and $I_0$ are related as

Two cables of copper are of equal lengths. One of them has a single wire of area of cross-section $A$, while other has 10 wires of cross-sectional area $A/10$ each. Give their suitability for transporting A.C. and D.C.