Calculate inductive reactance of coil in the following figure.

(i) impedance of the circuit.

(ii) Peak value of current in the circuit.

Find the capacitance of the capacitor.

What is the natural frequency of the LC circuit? What is the reactance of this circuit at this frequency?

(a) Why does a capacitor act as a short circuit at high frequencies?

(b) Why does a capacitor act as an open circuit at low frequencies?

[Hint: For tuning, the natural frequency i.e., the frequency of free oscillations of the LC circuit should be equal to the frequency of the radiowave.]

(i) $$ w L>\displaystyle\frac{1}{\omega C}$$,

(ii) $$w L<\displaystyle\frac{1}{\omega C}$$,

(iii) $$w L=\displaystyle\frac{1}{\omega C}$$.

What is the impedance of a capacitor of capacitance C in an AC circuit using source of frequency n Hz?

Write value of $$\dfrac{L}{1.1}+I$$.

Pure resistor and pure inductor.

(a)The pointer in the galvanometer deflects, when a bar magnet pushed or away from the coil connected to a galvanometer. Identify the phenomenon causing this deflection and write the factors on which the amount and direction of the deflection depends. State the laws describing this phenomenon.

(b) Sketch the change in flux, emf and force when a conducting rod PQ of resistance R and length l moves freely to and fro between A and C with speed v on a rectangular conductor placed in uniform magnetic field as shown in the figure.

(i) The frequency of the source.

(ii) The rms current through the resistor.

Find:

The current in the circuit

Find:

The capacitance $$C$$ of the capacitor

(a) Root mean square value of voltage.'

(b) Impedance of circuit.

(a) capacitance (b) inductance to be put in series to run the lamp

(c) how much pure resistance should be included in place of the above device so that lamp can run on its voltage?

(i)the capacitive reactance of the circuit.

(ii)an impedance of the circuit

(i) maximum value of current in the circuit,

(ii) root mean square value of current in the circuit,

(a) name the circuit element $$Y$$.

(b) calculate the rms value of current, if rms value of voltage is $$141V$$.

(c) what will happen if the ac source is replaced by a dc source?

An ideal inductor has the same reactance at $$100 Hz$$ frequency as the capacitor has at the same frequency. Find the value of inductance of the inductor.

The potential V and the unknown capacitance C.

What should be the frequency of the source such that current drawn in the circuit is maximum? What is this frequency called?

For a very high frequency AC supply, a capacitor behaves like a pure conductor.Why?

(i) $$\cfrac{1}{2}$$ time

(ii) $$\cfrac { \sqrt { 3 } }{ 2 } $$ time of its peak value

(i) At which frequency will its reactance be $$3140\Omega$$

(ii) What will be the capacity of the capacitor so that its reactance remain same at the same frequency?

(i) total reactance

(ii) impedance

(iii) power factor

(iv) average power

(i) resonant frequency

(ii) impedance of the circuit and peak value of current at resonant frequency

(iii) square mean root value of voltages at three components.

What is wattles current?

$$[R_{1}=25\Omega ,R_{2}=5\Omega ,L=10H,C=20\mu F]$$. Use $$e^{x}\simeq 1+x,x< < 1$$.

find the current through resistor $$R_2$$ in amperes.

(a) What is the maximum current in the coil?

(b) What is the time lag between the voltage maximum and the current maximum?

a) Which one of the two bulbs lights up earlier, when key k is closed and why?

b) What will be the comparative brightness of the two bulbs after sometime if the key K is kept closed and why?

(a) the $$rms$$ current in the circuit.

(b) the $$rms$$ potential differences across the capacitor, the resistor and the inductor, Note that the sum of the $$rms$$ potential difference across the three elements is greater than the $$rms$$ voltage of the source.

(i) Impedance of the circuit ,

(ii) Power factor angle ,

(iii) Power factor ,

(iv) Current ,

(v) Maximum current ,

(vi) Voltage across R ,

(vii) Voltage across C ,

(viii) Maximum voltage across R ,

(ix) Maximum voltage across C ,

(x) $$ < P > $$ ,

(xi) $$ < P_R > $$ ,

(xii) $$ < P_C > $$

(xiii) $$ i(t) , V_R (t) $$ and $$ V_C(t) $$

The open switch in Figure is thrown closed at $$t =0$$. Before the switch is closed, the capacitor is uncharged and all currents are zero. Determine the currents in $$L, \,C$$, and $$R$$, the emf across $$L$$, and the potential differences across $$C$$ and $$R$$

(a) at the instant after the switch is closed and

(b) long after it is closed.

The switch in Figure is connected to position a for a long time interval. At $$t = 0$$, the switch is thrown to position "b". After this time, what are (a) the frequency of oscillation of the LC circuit, (b) the maximum charge that appears on the capacitor, (c) the maximum current in the inductor, and (d) the total energy the circuit possesses at $$t = 3.00 \,s$$?

Consider an LC circuit in which $$L = 500 \,mH$$ and $$C = 0.100 \mu F$$. (a) What is the resonance frequency $$\omega_0$$?(b) If a resistance of $$1.00 k\Omega$$ is introduced into this circuit, what is the frequency of the damped oscillations? (c) By what percentage does the frequency of the damped oscillations differ from the resonance frequency?

Show that the rms value for the sawtooth voltage shown in Figure is $$\Delta V_{max}/\sqrt{3}$$.

A series RLC circuit has resonance angular frequency $$2.00 \times 10^3 \,rad/s$$. When it is operating at some input frequency, $$X_L = 12.0 \Omega$$ and $$X_C = 8.00 \Omega$$. (a) Is this input frequency higher than, lower than, or the same as the resonance frequency? Explain how you can tell.(b) Explain whether it is possible to determine the values of both L and C. (c) If it is possible, find L and C.If it is not possible, give a compact expression for the condition that L and C must satisfy.

A $$400-\Omega$$ resistor, an inductor, and a capacitor are in series with an AC source. The reactance of the inductor is $$700 \,\Omega$$, and the circuit impedance is $$760 \,\Omega$$. (a) What are the possible values of the reactance of the capacitor? (b) If you find that the power delivered to the circuit decreases as you raise the frequency, what is the capacitive reactance in the original circuit? (c) Repeat part (a) assuming the resistance is $$200 \,\Omega$$ instead of $$400 \,\Omega$$ and the circuit impedance continues to be $$760 \,\Omega$$.

A series RLC circuit has components with the following values: $$L = 20.0 \,mH, \,C = 100 \,nF, \,R = 20.0 \,\Omega$$, and $$\Delta V_{max} = 100 \,V$$, with $$\Delta v = \Delta V_{max} \sin \omega t$$. Find (a) the resonant frequency of the circuit, (b) the amplitude of the current at the resonant frequency, (c) the Q of the circuit, and (d) the amplitude of the voltage across the inductor at resonance.

A diode is a device that allows current to be carried in only one direction (the direction indicated by the arrowhead in its circuit symbol). Find the average power delivered to the diode circuit of Figure in terms of $$\Delta V_{rms}$$ and $$R$$.

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