مقسم ولتاژ

${\displaystyle V_{\mathrm {out} }={\frac {Z_{2}}{Z_{1}+Z_{2}}}\cdot V_{\mathrm {in} }}$

اثبات با استفاده از قانون اهم:

${\displaystyle V_{\mathrm {in} }=I\cdot (Z_{1}+Z_{2})}$

${\displaystyle V_{\mathrm {out} }=I\cdot Z_{2}}$

${\displaystyle I={\frac {V_{\mathrm {in} }}{Z_{1}+Z_{2}}}}$

${\displaystyle V_{\mathrm {out} }=V_{\mathrm {in} }\cdot {\frac {Z_{2}}{Z_{1}+Z_{2}}}}$

${\displaystyle H={\frac {V_{out}}{V_{in}}}={\frac {Z_{2}}{Z_{1}+Z_{2}}}}$

مقسم مقاومتی

${\displaystyle V_{\mathrm {out} }={\frac {R_{2}}{R_{1}+R_{2}}}\cdot V_{\mathrm {in} }}$

اگر R₁ = R₂ آنگاه

${\displaystyle V_{\mathrm {out} }={\frac {1}{2}}\cdot V_{\mathrm {in} }}$

اگر V_out=6V and V_in=9V، آنگاه:

${\displaystyle {\frac {V_{\mathrm {out} }}{V_{\mathrm {in} }}}={\frac {R_{2}}{R_{1}+R_{2}}}={\frac {6}{9}}={\frac {2}{3}}}$

برای R1:

${\displaystyle R_{1}={\frac {R_{2}\cdot V_{\mathrm {in} }}{V_{\mathrm {out} }}}-R_{2}=R_{2}\cdot ({{\frac {V_{\mathrm {in} }}{V_{\mathrm {out} }}}-1})}$

برای R2:

${\displaystyle R_{2}=R_{1}\cdot {\frac {1}{({{\frac {V_{\mathrm {in} }}{V_{\mathrm {out} }}}-1})}}}$

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