Resistive, Capacitive Circuit (RC-Circuit)
Category : JEE Main & Advanced
(1) Applied voltage : \[V=\sqrt{V_{R}^{2}+V_{C}^{2}}\]
(2) Impedance : \[Z=\sqrt{{{R}^{2}}+X_{C}^{2}}=\sqrt{{{R}^{2}}+{{\left( \frac{1}{\omega C} \right)}^{2}}}\]
(3) Current : \[i={{i}_{0}}\sin \,\left( \omega \,t+\varphi \right)\]
(4) Peak current : \[{{i}_{0}}=\frac{{{V}_{0}}}{Z}=\frac{{{V}_{0}}}{\sqrt{{{R}^{2}}+X_{C}^{2}}}\]\[=\frac{{{V}_{0}}}{\sqrt{{{R}^{2}}+\frac{1}{4{{\pi }^{2}}{{\nu }^{2}}{{C}^{2}}}}}\]
(5) Phase difference : \[\varphi ={{\tan }^{-1}}\frac{{{X}_{C}}}{R}={{\tan }^{-1}}\frac{1}{\omega CR}\]
(6) Power factor : \[\cos \varphi =\frac{R}{\sqrt{{{R}^{2}}+X_{C}^{2}}}\]
(7) Leading quantity : Current
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