In a given series $LCR$ circuit,$R = 4\,\Omega$,$X_L = 5\,\Omega$,and $X_C = 8\,\Omega$. The current:

In an $RL$ circuit,the current is $i = 100 \sin(314t) \ A$ and the voltage is $e = 200 \sin(314t + \pi/3) \ V$. If the resistance is $1 \ \Omega$,what is the reactance?

In a series $RLC$ circuit,the potential differences across $R, L$ and $C$ are $30 \,V, 60 \,V$ and $100 \,V$ respectively,as shown in the figure. The $e.m.f.$ of the source (in volts) is:

In an $ac$ circuit,the potential difference across an inductance and resistance joined in series are respectively $16\, V$ and $20\, V$. The total potential difference across the circuit is.......$V$

$A$ light bulb and an inductor coil are connected to an $AC$ source through a key as shown in the figure below. The key is closed and after some time an iron rod is inserted into the interior of the inductor. The glow of the light bulb

For an $LCR$ circuit driven at frequency $\omega $,the equation reads $L\frac{di}{dt} + Ri + \frac{q}{C} = V_i = V_m \sin \omega t$.
$(a)$ Multiply the equation by $i$ and simplify where possible.
$(b)$ Interpret each term physically.
$(c)$ Cast the equation in the form of a conservation of energy statement.
$(d)$ Integrate the equation over one cycle to find that the phase difference between $V$ and $i$ must be acute.