Shortcut Methods
JEE Main Level:
- Numerical 1:
- Shortcut Method: $$f_r=\frac{1}{2\pi}(\sqrt{1/L_1}+ \sqrt{1/L_2})$$
OR
$$f_r=\frac{1}{2\pi} \sqrt{\frac{1}{LC}(\frac{L_1+L_2}{L_1L_2})}$$
$$f_r=\frac{1}{2\pi\sqrt{(100\text{ mH})(100\mu \text{F})}}$$
- Numerical 2:
- Shortcut Method:
$$Q=\frac{\omega_{res}L}{R}=\frac{1}{R}\sqrt{\frac{L}{C}}$$
CBSE Board Level:
- Numerical 1:
- Shortcut Method: Resonant current $$I_res=\frac{V}{R}:Q:V_m$$
$$I_res=\frac{V}{R}$$
- Numerical 2:
- Shortcut Method: $$Q=\frac{\omega_{res}L}{R}= \frac{V_C}{IR}$$
$$V_C=QI_r =\frac{\omega_{res}L}{R}$$
