An LCR series circuit with a resistance of 100 ohm is connected to an AC source of 200 V (rms) and angular frequency 300 rad/s. When only the capacitor is removed, the current lags behind the voltage by 60°. When only the inductor is removed the current leads the
voltage by 60°. The average power dissipated is :
The current in a circuit varies with time as I = 2 √t . Then the rms value of the current for the interval t = 2 to t = 4 sec is
The graph shows variation of I with f for a series R-L-C network. Keeping L and C constant. If R
decreases :
(a) Maximum current (Im) increases
(b) Sharpness of the graph increases
(c) Quality factor increases
(d) Band width increases
A series LCR circuit containing \(5.0\text{ H}\) inductor, \(80 \mu\text{F}\) capacitor and \(40 \Omega\) resistor is connected to \(230\text{ V}\) variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be
The resonant angular frequency is \(\omega_0 = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{5 \times 80 \times 10^{-6}}} = 50\text{ rad/s}\) and the bandwidth is \(Delta \omega = \frac{R}{L} = \frac{40}{5} = 8\text{ rad/s}\). The half-power frequencies are \(omega_0 \pm \frac{\Delta \omega}{2} = 50 \pm 4\text{ rad/s}\), which gives \(46\text{ rad/s}\) and \(54\text{ rad/s}\).