# Fundamental Physics/Electricity/Electric circuits/Resistor circuit

 Voltage divider ${\displaystyle i={\frac {V}{R_{2}+R_{1}}}}$ ${\displaystyle V_{o}=iR_{2}=R_{i}{\frac {v_{i}}{R_{2}+R_{1}}}}$ ${\displaystyle {\frac {V_{o}}{V_{i}}}={\frac {R_{2}}{R_{2}+R_{1}}}}$ ${\displaystyle {\frac {V_{o}}{V_{i}}}={\frac {R_{2}}{R_{2}+R_{1}}}}$ Resistor in T configuration ${\displaystyle V=V_{2}{\frac {R_{1}}{R_{1}+R_{3}}}=V_{1}{\frac {R_{1}}{R_{2}+R_{1}}}}$ ${\displaystyle {\frac {V_{2}}{V_{1}}}={\frac {R_{1}+R_{3}}{R_{1}}}{\frac {R_{1}}{R_{2}+R_{3}}}}$ ${\displaystyle {\frac {V_{2}}{V_{1}}}={\frac {R_{1}+R_{3}}{R_{2}+R_{3}}}}$ Resistor in π configuration ${\displaystyle i_{1}=i_{2}+i_{3}}$ ${\displaystyle {\frac {v_{i}}{R_{1}}}={\frac {v_{i}-v_{o}}{R_{2}}}+{\frac {v_{o}}{R_{3}}}}$ ${\displaystyle {\frac {v_{i}}{v_{o}}}=({\frac {R_{3}}{R_{1}}})({\frac {R_{2}-R_{1}}{R_{2}-R_{3}}})}$ ${\displaystyle {\frac {v_{o}}{v_{i}}}=({\frac {R_{3}}{R_{1}}})({\frac {R_{2}-R_{1}}{R_{2}-R_{3}}})}$ Reistor in series and parallel ${\displaystyle R_{EQ}=(R_{1}\|R_{2})+R_{3}}$ ${\displaystyle R_{EQ}={R_{1}R_{2} \over R_{1}+R_{2}}+R_{3}}$ Transformation Δ - Y transformation ${\displaystyle R_{1}={\frac {R_{\mathrm {a} }R_{\mathrm {b} }}{R_{\mathrm {a} }+R_{\mathrm {b} }+R_{\mathrm {c} }}}}$ ${\displaystyle R_{2}={\frac {R_{\mathrm {b} }R_{\mathrm {c} }}{R_{\mathrm {a} }+R_{\mathrm {b} }+R_{\mathrm {c} }}}}$ ${\displaystyle R_{3}={\frac {R_{\mathrm {c} }R_{\mathrm {a} }}{R_{\mathrm {a} }+R_{\mathrm {b} }+R_{\mathrm {c} }}}}$ Y - Δ transformation ${\displaystyle R_{\mathrm {a} }={\frac {R_{1}R_{2}+R_{2}R_{3}+R_{3}R_{1}}{R_{2}}}}$ ${\displaystyle R_{\mathrm {b} }={\frac {R_{1}R_{2}+R_{2}R_{3}+R_{3}R_{1}}{R_{3}}}}$ ${\displaystyle R_{\mathrm {c} }={\frac {R_{1}R_{2}+R_{2}R_{3}+R_{3}R_{1}}{R_{1}}}}$