I = V i R 2 + R 1 {\displaystyle I={\frac {V_{i}}{R_{2}+R_{1}}}} V o = I R 2 = V i R 2 R 2 + R 1 {\displaystyle V_{o}=IR_{2}=V_{i}{\frac {R_{2}}{R_{2}+R_{1}}}} V o V i = R 2 R 2 + R 1 {\displaystyle {\frac {V_{o}}{V_{i}}}={\frac {R_{2}}{R_{2}+R_{1}}}} V o V i = R 2 R 2 + R 1 {\displaystyle {\frac {V_{o}}{V_{i}}}={\frac {R_{2}}{R_{2}+R_{1}}}}
V = V 2 R 1 R 1 + R 3 = V 1 R 1 R 2 + R 1 {\displaystyle V=V_{2}{\frac {R_{1}}{R_{1}+R_{3}}}=V_{1}{\frac {R_{1}}{R_{2}+R_{1}}}} V 2 V 1 = R 1 + R 3 R 1 R 1 R 2 + R 3 {\displaystyle {\frac {V_{2}}{V_{1}}}={\frac {R_{1}+R_{3}}{R_{1}}}{\frac {R_{1}}{R_{2}+R_{3}}}} V 2 V 1 = R 1 + R 3 R 2 + R 3 {\displaystyle {\frac {V_{2}}{V_{1}}}={\frac {R_{1}+R_{3}}{R_{2}+R_{3}}}} V 2 V 1 = R 1 + R 3 R 2 + R 3 {\displaystyle {\frac {V_{2}}{V_{1}}}={\frac {R_{1}+R_{3}}{R_{2}+R_{3}}}}
R 1 = R a R b R a + R b + R c {\displaystyle R_{1}={\frac {R_{\mathrm {a} }R_{\mathrm {b} }}{R_{\mathrm {a} }+R_{\mathrm {b} }+R_{\mathrm {c} }}}} R 2 = R b R c R a + R b + R c {\displaystyle R_{2}={\frac {R_{\mathrm {b} }R_{\mathrm {c} }}{R_{\mathrm {a} }+R_{\mathrm {b} }+R_{\mathrm {c} }}}} R 3 = R c R a R a + R b + R c {\displaystyle R_{3}={\frac {R_{\mathrm {c} }R_{\mathrm {a} }}{R_{\mathrm {a} }+R_{\mathrm {b} }+R_{\mathrm {c} }}}}
1. R≠0 và mạch điện hoạt động ở trạng thái cân bằng V L + V C + V R = 0 {\displaystyle V_{L}+V_{C}+V_{R}=0} L d 2 i d t 2 + 1 C ∫ i d t + i R = 0 {\displaystyle L{\frac {d^{2}i}{dt^{2}}}+{\frac {1}{C}}\int idt+iR=0} d 2 i d t 2 + R L d i d t + 1 L C i = 0 {\displaystyle {\frac {d^{2}i}{dt^{2}}}+{\frac {R}{L}}{\frac {di}{dt}}+{\frac {1}{LC}}i=0} d 2 i d t 2 = − R 2 L d i d t − 1 L C i {\displaystyle {\frac {d^{2}i}{dt^{2}}}=-{\frac {R}{2L}}{\frac {di}{dt}}-{\frac {1}{LC}}i} d 2 i d t 2 = − 2 α d i d t − β i {\displaystyle {\frac {d^{2}i}{dt^{2}}}=-2\alpha {\frac {di}{dt}}-\beta i} β = 1 T = 1 L C {\displaystyle \beta ={\frac {1}{T}}={\frac {1}{LC}}} α = β γ = R 2 L {\displaystyle \alpha =\beta \gamma ={\frac {R}{2L}}} T = L C {\displaystyle T=LC} γ = R C {\displaystyle \gamma =RC} Nghiệm phương trình Một nghiệm thực . α = β {\displaystyle \alpha =\beta } . i = A e − α t = A ( α ) {\displaystyle i=Ae^{-\alpha t}=A(\alpha )} Hai nghiệm thực . α > β {\displaystyle \alpha >\beta } . i = A e ( − α ± α − β ) t {\displaystyle i=Ae^{(-\alpha \pm {\sqrt {\alpha -\beta }})t}} Hai nghiệm phức . α < β {\displaystyle \alpha <\beta } . i = A e ( − α ± j β − α ) t = A ( α ) S i n ω t {\displaystyle i=Ae^{(-\alpha \pm j{\sqrt {\beta -\alpha }})t}=A(\alpha )Sin\omega t} A ( α ) = A e − α t {\displaystyle A(\alpha )=Ae^{-\alpha t}} ω = β − α {\displaystyle \omega ={\sqrt {\beta -\alpha }}} 2. R≠0 và mạch điện hoạt động ở trạng thái đồng bộ Z L = − Z C {\displaystyle Z_{L}=-Z_{C}} ω o = ± j 1 T {\displaystyle \omega _{o}=\pm j{\sqrt {\frac {1}{T}}}} T = L C {\displaystyle T=LC} Z t = Z L + Z C + Z R = Z R = R {\displaystyle Z_{t}=Z_{L}+Z_{C}+Z_{R}=Z_{R}=R} i = v R {\displaystyle i={\frac {v}{R}}} i ( ω = 0 ) = 0 {\displaystyle i(\omega =0)=0} i ( ω = ω o ) = v R {\displaystyle i(\omega =\omega _{o})={\frac {v}{R}}} i ( ω = 00 ) = 0 {\displaystyle i(\omega =00)=0} 3. R=0 và mạch điện hoạt động ở trạng thái cân bằng V L + V C = 0 {\displaystyle V_{L}+V_{C}=0} L d 2 i d t 2 + 1 C ∫ i d t = 0 {\displaystyle L{\frac {d^{2}i}{dt^{2}}}+{\frac {1}{C}}\int idt=0} d 2 i d t 2 + 1 L C i = 0 {\displaystyle {\frac {d^{2}i}{dt^{2}}}+{\frac {1}{LC}}i=0} d 2 i d t 2 = − 1 T i {\displaystyle {\frac {d^{2}i}{dt^{2}}}=-{\frac {1}{T}}i} i = A S i n ω t {\displaystyle i=ASin\omega t} ω = 1 T {\displaystyle \omega ={\sqrt {\frac {1}{T}}}} T = L C {\displaystyle T=LC} 4. R=0 và mạch điện hoạt động ở trạng thái đồng bộ Z L = − Z C {\displaystyle Z_{L}=-Z_{C}} ω o = ± j 1 T {\displaystyle \omega _{o}=\pm j{\sqrt {\frac {1}{T}}}} T = L C {\displaystyle T=LC} V L = − V C {\displaystyle V_{L}=-V_{C}} v ( θ ) = A S i n ( ω o t + 2 π ) − A S i n ( ω o t − 2 π ) {\displaystyle v(\theta )=ASin(\omega _{o}t+2\pi )-ASin(\omega _{o}t-2\pi )}
Ở trạng thái cân bằng V L + V C = 0 {\displaystyle V_{L}+V_{C}=0} L d 2 i d t 2 + 1 C ∫ i d t = 0 {\displaystyle L{\frac {d^{2}i}{dt^{2}}}+{\frac {1}{C}}\int idt=0} d 2 i d t 2 + 1 L C i = 0 {\displaystyle {\frac {d^{2}i}{dt^{2}}}+{\frac {1}{LC}}i=0} d 2 i d t 2 = − 1 T i {\displaystyle {\frac {d^{2}i}{dt^{2}}}=-{\frac {1}{T}}i} i = A S i n ω t {\displaystyle i=ASin\omega t} ω = 1 T {\displaystyle \omega ={\sqrt {\frac {1}{T}}}} T = L C {\displaystyle T=LC} Ở trạng thái đồng bộ Z L = − Z C {\displaystyle Z_{L}=-Z_{C}} ω o = ± j 1 T {\displaystyle \omega _{o}=\pm j{\sqrt {\frac {1}{T}}}} T = L C {\displaystyle T=LC} V L = − V C {\displaystyle V_{L}=-V_{C}} v ( θ ) = A S i n ( ω o t + 2 π ) − A S i n ( ω o t − 2 π ) {\displaystyle v(\theta )=ASin(\omega _{o}t+2\pi )-ASin(\omega _{o}t-2\pi )}
Mạch điện RL nối tiếp || V L + V R = 0 {\displaystyle V_{L}+V_{R}=0} L d i ( t ) d t + i ( t ) R = 0 {\displaystyle L{\frac {di(t)}{dt}}+i(t)R=0} d i ( t ) d t = − 1 T i ( t ) {\displaystyle {\frac {di(t)}{dt}}=-{\frac {1}{T}}i(t)} T = L R {\displaystyle T={\frac {L}{R}}} ∫ d i ( t ) i ( t ) = − 1 T ∫ d t {\displaystyle \int {\frac {di(t)}{i(t)}}=-{\frac {1}{T}}\int dt} L n i ( t ) = − 1 T + c {\displaystyle Lni(t)=-{\frac {1}{T}}+c} i ( t ) = A e − t T + c = A e − t T {\displaystyle i(t)=Ae^{-{\frac {t}{T}}+c}=Ae^{-{\frac {t}{T}}}} A = e c {\displaystyle A=e^{c}}
Mạch điện bộ lọc tần số thấp || v o v i = R R + j ω L = 1 1 + j ω L R = 1 1 + j ω T {\displaystyle {\frac {v_{o}}{v_{i}}}={\frac {R}{R+j\omega L}}={\frac {1}{1+j\omega {\frac {L}{R}}}}={\frac {1}{1+j\omega T}}} T = L R {\displaystyle T={\frac {L}{R}}} ω o = 1 T = R L = 2 π f o {\displaystyle \omega _{o}={\frac {1}{T}}={\frac {R}{L}}=2\pi f_{o}} v o ( ω = 0 ) = v i {\displaystyle v_{o}(\omega =0)=v_{i}} v o ( ω = ω o ) = v i 2 {\displaystyle v_{o}(\omega =\omega _{o})={\frac {v_{i}}{2}}} v o ( ω = 00 ) = 0 {\displaystyle v_{o}(\omega =00)=0}
v o v i = j ω L R + j ω L = j ω L R 1 + j ω L R = j ω T 1 + j ω T {\displaystyle {\frac {v_{o}}{v_{i}}}={\frac {j\omega L}{R+j\omega L}}={\frac {j\omega {\frac {L}{R}}}{1+j\omega {\frac {L}{R}}}}={\frac {j\omega T}{1+j\omega T}}} T = L R {\displaystyle T={\frac {L}{R}}} ω o = 1 T = R L = 2 π f {\displaystyle \omega _{o}={\frac {1}{T}}={\frac {R}{L}}=2\pi f} v o ( ω = 0 ) = 0 {\displaystyle v_{o}(\omega =0)=0} v o ( ω = ω o ) = v i 2 {\displaystyle v_{o}(\omega =\omega _{o})={\frac {v_{i}}{2}}} v o ( ω = 0 ) = v i {\displaystyle v_{o}(\omega =0)=v_{i}}
C d v d t + v R = 0 {\displaystyle C{\frac {dv}{dt}}+{\frac {v}{R}}=0} d v d t = − 1 T v {\displaystyle {\frac {dv}{dt}}=-{\frac {1}{T}}v} T = R C {\displaystyle T=RC} ∫ d v v = − 1 T ∫ d t {\displaystyle \int {\frac {dv}{v}}=-{\frac {1}{T}}\int dt} L n v = − 1 T + c {\displaystyle Lnv=-{\frac {1}{T}}+c} v = e − 1 T t + c = A e − 1 T t {\displaystyle v=e^{-{\frac {1}{T}}t+c}=Ae^{-{\frac {1}{T}}t}}
v o v i = 1 j ω C R + 1 j ω C = 1 j ω R C + 1 = 1 1 + j ω T {\displaystyle {\frac {v_{o}}{v_{i}}}={\frac {\frac {1}{j\omega C}}{R+{\frac {1}{j\omega C}}}}={\frac {1}{j\omega RC+1}}={\frac {1}{1+j\omega T}}} T = R C {\displaystyle T=RC} ω o = 1 T = 1 R C = 2 π f {\displaystyle \omega _{o}={\frac {1}{T}}={\frac {1}{RC}}=2\pi f} v o ( ω = 0 ) = v i {\displaystyle v_{o}(\omega =0)=v_{i}} v o ( ω = ω o ) = v i 2 {\displaystyle v_{o}(\omega =\omega _{o})={\frac {v_{i}}{2}}} v o ( ω = 00 ) = 0 {\displaystyle v_{o}(\omega =00)=0}
T = R C {\displaystyle T=RC} ω o = 1 T = 1 R C {\displaystyle \omega _{o}={\frac {1}{T}}={\frac {1}{RC}}} v o ( ω = 0 ) = 0 {\displaystyle v_{o}(\omega =0)=0} v o ( ω = ω o ) = v i 2 {\displaystyle v_{o}(\omega =\omega _{o})={\frac {v_{i}}{2}}} v o ( ω = 00 ) = v i {\displaystyle v_{o}(\omega =00)=v_{i}}
to 
