CBSE Class 12-science Answered
EXPLAIN LC OSCILLATIONS AND ALSO WATTLESS AND WATTFULL CURRENT WITH THE HELP OF DIAGRAM
Asked by pardeepkumar2281 | 04 Oct, 2018, 09:44: PM
Expert Answer
Capacitor stores electrical energy. Inductor stores magentic energy.
when a initially charged capacitor is connected to inductor, as shown in figure, the charge on the capacitor and
current in the circuit exhibit the phenomenon of electrical oscillations similar to oscillation in mechanical system.
Let a capacitor be charged qm and connected to inductor at t=0. The charge on the capacitor keep on decreasing
giving rise to currentin the circuit. Let q be the charge at capacitor and i be the current in the circuit at given time t.
Since di/dt is positive, induced emf in inductor will have polarity as shown in figure.
By Kirchoffs rule we have
...........................(1)
i = -(dq/dt) in this case ( as charge decreases current increases ), then we have
............................(2)
Eqn.(2) is similar to Simple Harmonic Motion, hence charge and current oscillates with natural frequency
Solution to eqn.(2) gives the charge at a given time t ,
Initially all the energy is stored in the form of electrical energy in the capacitor.
Then charge keep on decreasing and current will be established in the circuit.
Now inductor start storing the energy in the form of magnetic field.
When all the energy is transferred and no charge is present in the capacitor, capacitor starts charging in the
reverse direction using the stored energy of inductor till all the energy is transferred from inductor to capacitor.
Then the cycle repeats and oscillation is established in the circuit in this way.
-----------------------------
In RLC circuit, applied voltage v = vm sin(ωt) drives the current i = im sin(ωt+φ)
power in the circuit, p = v×i = vm im sin(ωt) sin(ωt+φ) ....................(2)
where φ is phase angle given by, , XC and XL are capacitive and inductive reactance
simplifying by trignometry and averaging eqn.(2) over one cycle, we get average power as
average power dissipation depends on phase angle φ in addition to current and voltage.
In a purely inductive and capacitive circuit, phase angle φ=90º, that makes power dissipation zero though
there is a current circulating in the circuit. This current is known as wattless current.
In RLC circuit, I×cosφ is known as wattfull current
Answered by Thiyagarajan K | 05 Oct, 2018, 08:53: PM
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