Resistive Circuits

calendar_today January 30, 2025 article 254 words access_time 3 min replay Modified April 2, 2025

Table of Contents

Kirchoff’s Laws

$$\sum V_{\text{drop}}=\sum V_{\text{rise}}$$

The sum of voltages sources and drops for any loop is zero
- Find the voltage/current for elements in series
- Based on the Law of Conservation of Energy

$$\sum i_{\text{in}} = \sum i_{\text{out}}$$

The sum of currents entering a node is zero
- Find the current for a loop
- Based on the Law of Conservation of Charge

$$ V_{n} = V_{s}R_{n}\left(\sum_{i=1}^N R_{i}\right)^{-1} $$

$$ i_{n} = i_{s}\left(\frac{1}{R_{n}}\right)\left(\sum_{i=1}^N \frac{1}{R_{i}}\right)^{-1} $$

$$i = GV$$

Current division across branches can be done with conductance values
- Use the formula for voltage division, but replace the resistances with conductances and voltage with current

$$i_{n} = i_{s}G_{n}\left(\sum_{i=1}^N G_{i}\right)^{-1}$$

$$V_{n} = V_{s}\left(\frac{1}{G_{n}}\right)\left(\sum_{i=1}^N \frac{1}{G_{i}}\right)^{-1}$$

Current sources may only be configured in parallel with one another
Current sources in parallel have the same voltage
Current sources in parallel can be combined to form one equivalent current source

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