Series circuit of n resistors. |
The total resistance of a series circuit of several resistors \(R_{Total}\) is calculated by... $$R_{Total} = R_1 + R_2 +....+R_n$$ By applying the Kirchhoff's Voltage Law (KVL) you get for the total voltage \(U_{Total}\)... $$U_{Total} = U_1 + U_2 +....+ U_n$$ and by applying Kirchhoff's Current Law (KCL) you know that the same current flows through all resistors.... $$I_1 = I_2 = .... = I_n.$$
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Special Cases Series circuit of \(N\) identical resistors... $$ R_{Total} = NR.$$ |
Parallel circuit of n resistors. |
The total resistance of a parallel circuit of n resistors \(R_{Total}\) is calculated by... $${1 \over R_{Total}} = {1 \over R_1} + {1 \over R_2} +....+ {1 \over R_n}$$ By applying the Kirchhoff's Voltage Law (KVL) you get that the same voltage applies to all resistors.... $$U_1 = U_2 = .... = U_n$$ and by applying Kirchhoff's Current Law (KCL) you get for the total current \(I_{Total}\)... $$I_{Total} = I_1 + I_2 +....+ I_n.$$
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Special Cases Parallel circuit of two resistors... $$ R_{Total} = {{R_1R_2} \over {R_1 + R_2}}$$ Parallel circuit of \(N\) identical resistors... $$ R_{Total} = {{R} \over {N}}$$ |
| Definition | Unit | |
| \(R_{Total}\) | Total Resistance | Ohm [Ω] |
| \(R_i\) | Single Resistance | Ohm [Ω] |
| \(U_{Total}\) | Total Voltage | Volt [V] |
| \(U_i\) | Single Voltage | Volt [V] |
| \(I_{Total}\) | Total Current | Ampere [A] |
| \(I_i\) | Single Current | Ampere [A] |
| \(N\) | Number Resistors |
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