Shortcut Methods
Shortcuts and Tricks
1. Resonant Frequency
$$f_r = \frac{1}{2\pi\sqrt{LC}}$$
Remember:
- Resonant frequency is inversely proportional to the square root of both inductance and capacitance.
- Higher the values of L and C, Lower is the resonant frequency.
2. Time Constant
$$ \tau = RC$$
Remember:
- Time constant is simply the product of resistance and capacitance.
- Higher the resistance, higher the time constant.
- Higher the capacitance, higher the time constant.
3. Initial Current
$$ I_{initial} = \frac{V_0}{R} $$
Remember:
- Initial current is the current flowing in the circuit at t=0, and it is determined solely by the voltage source and resistance.
- The inductance and capacitance have no effect on the initial current.
4. Voltage across Capacitor at t=0
$$V_C(0)=0,$$
Remember:
- At t=0, the capacitor is uncharged, so the voltage across it is zero.
- Current would start flowing through the resistor and charging the capacitor immediately, but the voltage across the capacitor at t=0 is still 0.
5. Energy stored in Inductor at t=0
$$E_L (0) = 0$$
Remember:
- At t=0, the inductor cannot store any energy because the current through it is still 0.
- The energy starts getting stored in the inductor as current starts flowing through it, but at t=0, the energy is still zero.
