Advertisements
Advertisements
Question
If the rms current in a 50 Hz ac circuit is 5 A, the value of the current 1/300 seconds after its value becomes zero is ______.
Options
`5sqrt(2)` A
`5sqrt(3/2)` A
`5/6` A
`5/sqrt(2)` A
Solution
If the rms current in a 50 Hz ac circuit is 5 A, the value of the current 1/300 seconds after its value becomes zero is `underline(5sqrt(3/2) A)`.
Explanation:
Equation for i and V: Alternating current or voltage varying as sine function can be written as
`i = i_0 sin ωt = i_0 sin 2piv t = i_0 sin (2pi)/T t`
And `V = V_0 sin ωt = V_0 sin 2pivt = V_0 sin (2pi)/T t`
Where I and V are instantaneous values of current and voltage,
i0 and V0 are peak values of current and voltage
ω = Angular frequency on rad/sec, v = Frequency in Hz
T = TIme peroid
`I_(ωt) = I = sqrt(2)I_0 = 5sqrt(2)A`
`I = I_0 sin ωt`
At `t = 1/300 sec, I = 5sqrt(2) sin 2 pivt = 5sqrt(2) sin 2pi xx 50 xx 1/300`
= `5sqrt(2) sin pi/3 = 5sqrt(2) sin 60^circ`
= `52 - sqrt(3)sqrt(2)` = 532
= `5sqrt(3/2) A`
APPEARS IN
RELATED QUESTIONS
A source of ac voltage v = v0 sin ωt, is connected across a pure inductor of inductance L. Derive the expressions for the instantaneous current in the circuit. Show that average power dissipated in the circuit is zero.
The current in a discharging LR circuit without the battery drops from 2.0 A to 1.0 A in 0.10 s. (a) Find the time constant of the circuit. (b) If the inductance of the circuit 4.0 H, what is its resistance?
(i) An a.c. source of emf ε = 200 sin omegat is connected to a resistor of 50 Ω . calculate :
(1) Average current (`"I"_("avg")`)
(2) Root mean square (rms) value of emf
(ii) State any two characteristics of resonance in an LCR series circuit.
In a series, LCR circuit, obtain an expression for the resonant frequency,
In a series LCR circuit the voltage across an inductor, capacitor and resistor are 20 V, 20 V and 40 V respectively. The phase difference between the applied voltage and the current in the circuit is ______.
The resonant frequency of a RF oscillator is 1 MHz and its bandwidth is 10 kHz. The quality factor will be :
A series LCR circuit containing 5.0 H inductor, 80 µF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be ______.
Consider the LCR circuit shown in figure. Find the net current i and the phase of i. Show that i = v/Z`. Find the impedance Z for this circuit.
