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An ac circuit, the current is given by i = 4 sin (100pt + 30º) ampere. The current becomes maximum first time (after t = 0) at t equal to
  • a)
    (1/200) sec
  • b)
    (1/300) sec
  • c)
    (1/50) sec
  • d)
    None of the above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An ac circuit, the current is given by i = 4 sin (100pt + 30º) am...
i=4sin(100πt+ π/6)
For I to be maximum
di/dt=0
therefore,4x100π(cos(100πt+π/6)=0
therefore, ωs(100πt+ π/6)=0
for the first time cosθ=0 at π/2
⇒ 100πt+ π/6= π/2
⇒ 100πt= π/3
⇒ πt= π/300
T=1/300
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Most Upvoted Answer
An ac circuit, the current is given by i = 4 sin (100pt + 30º) am...
To find the voltage in the circuit, we need to use Ohm's law and the relationship between voltage and current in an AC circuit:

V = I * Z

where V is the voltage, I is the current, and Z is the impedance of the circuit.

In an AC circuit, the impedance is a combination of resistance, capacitance, and inductance, and is given by:

Z = R + j(Xc - Xl)

where R is the resistance, Xc is the capacitive reactance, and Xl is the inductive reactance.

Assuming a purely resistive circuit, where there is no capacitance or inductance, the impedance is simply the resistance:

Z = R

So, if we know the resistance of the circuit, we can find the voltage by multiplying the current by the resistance.

Let's assume that the resistance of the circuit is 10 ohms. Then, the voltage is:

V = I * R
V = (4 sin (100pt + 30)) * 10
V = 40 sin (100pt + 30)

Thus, the voltage in the circuit is V = 40 sin (100pt + 30).
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Read the following text and answer the following questions on the basis of the same:Tuning a radio set: In essence the simplest tuned radio frequency receiver is a simple crystal set. Desired frequency is tuned by a tuned coil / capacitor combination, and then the signal is presented to a simple crystal or diode detector where the amplitude modulated signal, is demodulated. This is then passed straight to the headphones or speaker. In radio set there is an LC oscillator comprising of a variable capacitor (or sometimes a variable coupling coil), with a knob on the front panel to tune the receiver. Capacitor used in old radio sets is gang capacitor. It consists of two sets of parallel circular plates one of which can rotate manually by means of a knob. The rotation causes overlapping areas of plates to change, thus changing its capacitance. Air gap between plates acts as dielectric. The capacitor has to be tuned in tandem corresponding to the frequency of a station so that the LC combination of the radio set resonates at the frequency of the desired station.When capacitive reactance (XC) is equal to the inductive reactance (XL), then the resonance occurs and the resonant frequency is given by ω0 = 1/√LCcurrent amplitude becomes maximum at the resonant frequency. It is important to note that resonance phenomenon is exhibited by a circuit only if both L and C are present in the circuit. Only then do the voltages across L and C cancel each other (both being out of phas e) and the Current amplitude is Vm/R the total source voltage appearing across R. This means that we cannot have resonance in a RL or RC circuit.Resonance may occur in

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