Advertisements
Advertisements
प्रश्न
An a.c. source of voltage V = V0 sin ωt is connected to a series combination of L, C, and R. Use the phasor diagram to obtain the expression for an impedance of a circuit and the phase angle between voltage and current. Find the condition when current will be in phase with the voltage. What is the circuit in this condition called?
उत्तर
i)
Voltage of the source is given as
I0→" data-mce-style="position: relative;">V=V0sinωtI0→
Let current of the source be " data-mce-style="position: relative;">I=I0sinωt
The maximum voltage across R is `vec(V_R)=vec(V_0)R` represented along OX.
The maximum voltage across L is `vec(V_L)=vec(I_0) X_L`represented along OY and is 90° ahead of `vec(I_0)`
The maximum voltage across C is `vec(V_C)=vec(I_0) X_C`represented along OC and is lagging behind `vec(I_0)`by 900
The voltage across L and C has a phase difference of 180°
Hence, reactive voltage is`vec(V_L)-vec(V_C)`represented by OB
The vector sum of`vec(V_R), vec(V_L) "and "vec(V_C)`resultant of OA and OB', represented along OK
`OK=V_0=sqrt(OA^2+OB^2)`
`=>V_0=sqrt(V_R2+(V_L-V_C)^2)=sqrt(I_0R^2+(I_0X-V_C)^2)`
`=>V_0=I_0sqrt(R^2+(X_L-X_C)^2)`
The impedance can be calculated as follows:
`Z=V_0/I_0=sqrt(R^2+(X_L-X_C)^2)`
When XL = XC, the voltage and current are in the same phase. In such a situation, the circuit is known as the non-inductive circuit.
संबंधित प्रश्न
When an AC source is connected to an ideal inductor show that the average power supplied by the source over a complete cycle is zero.
In a series LR circuit, XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL = XC is put in series, the power factor becomes P2. Calculate P1/P2
An A.C. generator generating an emf of ε = 300 sin (100 πt) V is connected to a series combination of 16μ F capacitor, 1 H inductor and 100 Ω resistor.
Calculate :
1) An impedance of the circuit at the given frequency.
2) Resonant frequency `f_0`
3)Power factor at the resonant frequency `f_0`.
A resistance is connected to an AC source. If a capacitor is included in the series circuit, will the average power absorbed by the resistance increase or decrease? If an inductor of small inductance is also included in the series circuit, will the average power absorbed increase or decrease further?
A series AC circuit has a resistance of 4 Ω and a reactance of 3 Ω. The impedance of the circuit is
Consider the situation of the previous problem. Find the average electric field energy stored in the capacitor and the average magnetic field energy stored in the coil.
Following figure shows a typical circuit for a low-pass filter. An AC input Vi = 10 mV is applied at the left end and the output V0 is received at the right end. Find the output voltage for ν = 10 k Hz, 1.0 MHz and 10.0 MHz. Note that as the frequency is increased the output decreases and, hence, the name low-pass filter.
Suppose the circuit has a resistance of 15 Ω. Obtain the average power transferred to each element of the circuit, and the total power absorbed.
Quality factor and power factor both have the dimensions of ______.
A 100 Ω electric iron is connected to 200 V, 50 Hz ac source. Calculate average power delivered to iron, peak power and energy spent in one minute?
