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P Pankaj Sanodiya
The inductance of the inductor  The capacitance of the capacitor  Voltage supply  Frequency of voltage supply . Here, we have   Impedance   Now, Current in the circuit will be  where,  The negative sign is just a matter of the direction of current.so, here   But, since the value of R is zero(since our circuit have only L and C) Hence   Now,  RMS value of this current:  .

P Pankaj Sanodiya
As we know, in the case of a parallel RLC circuit:   The current will be minimum when Which is also the condition of natural frequency. Hence the total current is minimum when source frequency is equal to the natural frequency. RMS value of current in R  RMS value in Inductor RMS value in capacitor Capacitor current and inductor current will cancel out each other so the current flowing in...

P Pankaj Sanodiya
Given, The capacitance of the capacitor  The resistance of the circuit  Voltage supply  Frequency of voltage supply  The maximum current in the circuit Hence maximum current in the circuit is 3.9A. b) In the case of capacitor, we have  So, So the time lag between max voltage and max current is : At high frequencies,  tends to zero. which indicates capacitor acts as a conductor at high...

P Pankaj Sanodiya
In the case of a capacitor, we have  So, So the time lag between max voltage and the max current is :

P Pankaj Sanodiya
Given, The capacitance of the capacitor  The resistance of the circuit  Voltage supply  Frequency of voltage supply  The maximum current in the circuit Hence maximum current in the circuit is 3.24A.

P Pankaj Sanodiya
Given, The inductance of the coil  the resistance of the coil  Supply voltage  Supply voltage frequency a) Now, as we know peak voltage = (RMS Voltage) Peak voltage  Now,  The impedance of the circuit : Now peak current in the circuit : Hence peak current is  in the circuit. The current in the circuit is very small, which is one of the indications of inductor working as a nearly open circuit...

P Pankaj Sanodiya
Let the voltage  in the circuit be   and  Current in the circuit be  Where  is the phase difference between voltage and current.  V is maximum At t = 0  is maximum At      Hence, the time lag between voltage maximum and the current maximum is  . For phase difference   we have  Hence time lag between the maximum voltage and the maximum current is

P Pankaj Sanodiya
Given, The inductance of the coil  the resistance of the coil  Supply voltage  Supply voltage frequency Now, as we know peak voltage = (RMS Voltage) Peak voltage    The impedance of the circuit : Now peak current in the circuit : Hence peak current is 1.82A in the circuit.

P Pankaj Sanodiya
If the resistance is added to the circuit, the whole energy will dissipate as heat eventually. energy will keep moving between the capacitor and inductor with reducing in magnitude in each cycle and eventually all energy will be dissipated.

P Pankaj Sanodiya
The energy will be shared equally when the energy in the capacitor is half of the maximum energy it can store.i.e. From Here, we got So Now, we know the charge on the capacitor, we can calculate time for which From here,   Hence for these times, the total energy will be shared equally between capacitor and inductor.

P Pankaj Sanodiya
The stored energy will we purely magnetic when the pure electrical stored is zero. i.e. when the charge on the capacitor is zero, all energy will be stored in the inductor. So, t for which charge on the capacitor is zero is Hence at these times, the total energy will be purely magnetic.

P Pankaj Sanodiya
at any instant, the charge on the capacitor is: Where time period :   Now, when the total energy is purely electrical, we can say that    this is possible when   Hence Total energy will be purely electrical(stored in a capacitor) at  .

P Pankaj Sanodiya
Given, The inductance of the inductor:   The capacitance of the capacitor :   The initial charge on the capacitor: The natural angular  frequency of the circuit: Hence the natural angular frequency of the circuit is . The natural frequency of the circuit: Hence natural frequency of the circuit is 159Hz.

P Pankaj Sanodiya
Given, The inductance of the inductor:   The capacitance of the capacitor :   The initial charge on the capacitor: Total energy present at the initial moment: Hence initial energy in the circuit is 1J. Since we don't have any power-consuming element like  resistance in the circuit, the energy will be conserved

P Pankaj Sanodiya
Potential difference across any element =  NOW, The potential difference across capacitor: Potential difference across the inductor  The potential difference across Resistor  Potential difference across LC combination Hence at resonating frequency potential difference across LC combination is zero.

P Pankaj Sanodiya
Given, Variable frequency supply voltage  = 230V Inductance  Capacitance  Resistance  Now, The impedance of the circuit is    at Resonance Condition : Hence, Impedance at resonance is 40. Now, at resonance condition, impedance is minimum which means current is maximum which will happen when we have a peak voltage, so Current in the Resonance circuit is Given by  Hence amplitude of the current...

P Pankaj Sanodiya
Given, Variable frequency supply voltage  = 230V Inductance  Capacitance  Resistance  a) Resonance angular frequency in this circuit is given by : Hence this circuit will be in resonance when supply frequency is 50 rad/sec.

P Pankaj Sanodiya
Given,  Range of the frequency in which radio can be tune =  The effective inductance of the Circuit =  Now, As we know,   where  is tuning frequency. For getting the range of the value of a capacitor, let's calculate the two values of the capacitor, one maximum, and one minimum. first, let's calculate the minimum value of capacitance which is the case when tuning frequency = 800KHz. Hence...