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Counter-Strike: Source (2004)

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When a capacitor of capacity \( C \) is In a parallel resonance circuit, a coil of inductance carrying a charge \( q \), electrostatic energy, \( U_{E}=\frac{q^{2}}{2 C} \) is \( \quad L \) and a condenser of capacity \( C \) are joined in parallel to a source of alt. e.m.f. At parallel resonance frequency stored in it. When the charged capacitor is connected \( \quad v=\frac{1}{2 \pi \sqrt{L C}}, I=0 \). The circuit does not allow any to an inductor, the energy stored in the condenser appears in the form of magnetic field energy, current to flow through. This is why such a circuit is \( U_{B}=\frac{1}{2} L I^{2} \). As soon as discharge of capacitor is called filter circuit or rejector circuit or even anti- resonance circuit.
complete, current stops and magnetic flux linked with Average power associated with a non-inductive \( L \) starts collapsing. Therefore, an induced emf develops, circuit is \( P=E_{v} I_{v} \). Again, over a complete cycle, which starts recharging the capacitor in the opposite Average power associated with an inductor \( = \) Zero. direction. The recharging is also opposed and hence Average power associated with a capacitor=Zero. delayed. In this way, \( L C \) oscillations are set up. If the In general, in an inductive circuit, average power circuit has no resistance, no loss of energy would occur. over a complete cycle is \( P=E_{v} I_{v} \cos \phi \) These are called undamped oscillations, whose frequency is
Here, \( \cos \phi=\frac{R}{Z} \) is called Power Factor of the \( v=\frac{1}{2 \pi \sqrt{L C}} \quad \) circuit. Power factor is positive and its value is \( \leq 1 \).
A circuit in which inductance \( L \), capacitance \( C \) The current which consumes no power for its and resistance \( R \) are connected in series and the circuit maintenance in the circuit is called Wattless current or admits maximum current corresponding to a given Idle current. In any a.c. circuit, \( \left(I_{v} \sin \phi\right) \) is called the frequency of a.c. is called series resonance circuit. Idle component or Wattless component of a.c.
The impedance \( Z \) of an \( R L C \) circuit is
A transformer is an electrical device, which is used
\[
Z=\sqrt{R^{2}+\left(\omega L-\frac{1}{\omega C}\right)^{2}}
\]
for changing a.c. voltages. It is based on the principle of mutual induction.
When \( X_{L}=X_{C} \) \( \frac{E_{s}}{E_{p}}=\frac{n_{s}}{n_{p}}=K= \) transformer ratio i.e. \( \omega L=\frac{1}{\omega C}, \omega=\sqrt{\frac{1}{L C}} \) or \( v=\frac{1}{2 \pi} \sqrt{\frac{1}{L C}} \quad \) If we assume that no energy is lost, then \( Z=\sqrt{R^{2}+0}=R= \) minimum. \( \quad \quad E_{s} I_{s}=E_{p} I_{p} \) or \( I_{s}=\frac{E_{p}}{E_{s}} I_{p}=\frac{n_{p}}{n_{s}} I_{p}=\frac{I_{p}}{K} \) Therefore, current, \( I_{0}=\frac{E_{0}}{Z}=\frac{E_{0}}{R}= \) maximum. For a step up transformer, \( K1 \therefore E_{s}E_{p} \) This frequency is called series resonance frequency. The series resonance circuit is practically \( I_{s}=\frac{I_{p}}{K} \quad \therefore I_{s}I_{p} \) used in radio and T.V. receiver sets.
The reverse is true for a step down transformer.
The \( Q \) factor of resonance circuit is the ratio of The major energy losses in a transformer are Copper voltage developed across the inductance or capacitance losses, Iron loss, leakage of magnetic flux, Hysterisis at resonance to the impressed voltage applied across \( R \). loss etc.
\[
Q=\frac{1}{R} \sqrt{\frac{L}{C}} \text {. A transformer is used in almost all a.c. operations. }
\]
\( Q \) is just a number having no dimensions. It is given, one labelled Assertion (A) and the other also called voltage amplification factor of the circuit. labelled Reason (R).
Select the correct answer to these questions from the codes \( (a),(b),(c) \) and \( (d) \) as given below :
(a) Both \( \mathrm{A} \) and \( \mathrm{R} \) are true and \( \mathrm{R} \) is the correct explanation of \( \mathrm{A} \).
(b) Both \( \mathrm{A} \) and \( \mathrm{R} \) are true but \( \mathrm{R} \) is not the correct explanation of \( \mathrm{A} \).
(c) \( \mathrm{A} \) is true, but \( \mathrm{R} \) is false.
(d) \( \mathrm{A} \) is false, but \( \mathrm{R} \) is true.
Assertion. Power factor of the oscillator circuit is \( \cos \phi=\frac{R}{Z} \), where symbols have usual meaning.
Reason. In any a.c. circuit, the component of current \( =I_{v} \sin \phi \) is called the Idle component or Wattless component of \( a . c \).
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