In an electrical circuit R, L, C and an a.c.voltage source are all connected in series.When L is removed from the circuit, the phase difference between the voltage and the currentin the circuit is $$\pi /3$$. If instead, C is removed from the circuit the phase difference is again $$\pi /3$$. The power factor of the circuit is
The Power factor of a circuit is defined as:
$$cos\ \phi=\dfrac{Z}{R}$$
Here, $$Z$$ is the impedance of the circuit and $$R$$ is the resistance connected.
In the first case, the inductor is removed from the circuit. Therefore, the phase difference in the voltage and current due to resistance and capacitor will be:
$$tan\ \phi_1=\dfrac{X_C}{R}$$
$$\Rightarrow tan\dfrac\pi3=\dfrac{X_C}{R}$$
In the second case, the Capacitor is removed. So, the phase difference between the current and voltage is:
$$tan\ \phi_2=\dfrac{X_L}{R}$$
$$\Rightarrow tan\dfrac\pi3=\dfrac{X_L}{R}$$
Since the phase difference is the same in both cases, the impedance of the capacitor and inductor will be the same.
$$X_L=X_C$$
Therefore, the total impedance of the circuit will be:
$$Z=\sqrt{R^2+(X_L-X_C)^2}\\\Rightarrow Z=R$$
The power factor of the whole circuit is:
$$cos\ \phi=\dfrac{R}{R}\\\implies cos\phi=1$$
Option $$(A)$$ is correct.
For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor C', when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor C', must have been connected in parallel with C and has a magnitued
The potential differences of the resistance, the capacitor and the inductor are $$80 V, 40 V$$ and $$100 V$$ respectively in an $$L.C.R$$ circuit. The power factor of the circuit is
The power factor is an L-C-R circuit at resonance is
If the power factor in a circuit is unity, then the impedance of the circuit is
In L-C circuit power factor at resonance is:
In an L.C.R series resonant circuit, the power factor is __________.
A coil has a resistance of $$ 10\Omega $$ and an inductance of $$0.4$$ henry. It is connected to an AC source of $$6.5V,\dfrac{30}{\pi }$$Hz. Find the average power consumed in the circuit.
The power in A.C. circuit is given by $$P=E_{rms}i_{rms}\cos\phi$$. The value of power factor $$\cos\phi$$ in series LCR circuit at resonance is?
A resistor of $$500 \Omega$$, an inductance of $$0.5 H$$ are in series with an a.c. which is given by $$V = 100\sqrt{2} \sin{\left(1000 t\right)}$$. The power factor of the combination is
Above figure, shows an $$ac$$ generator connected to a “black box” through a pair of terminals. The box contains an $$RLC$$ circuit, possibly even a multiloop circuit, whose elements and connections we do not know. Measurements outside the box reveal that, $$\xi \left ( t \right )=\left ( 75.00 \right )\sin \omega _{d}t$$ and $$i\left ( t \right )=\left ( 1.20A \right )\sin\left ( \omega _{d}t+42.0^{0} \right )$$. (a) What is the power factor? (b) Does the current lead or lag the $$emf$$? (c) Is the circuit in the box largely inductive or largely capacitive? (d) Is the circuit in the box in resonance? (e) Must there be a capacitor in the box? (f) An inductor? (g) A resistor? (h) At what average rate is energy delivered to the box by the generator? (i) Why don’t you need to know $$\omega _{d}$$ to answer all these questions?