Ohm's law and conductance

Every resistor obeys one linear relationship, and its inverse is just as useful.

• Ohm's law is v = iR: the voltage across a resistor is proportional to the current, with resistance R (in Ω) as the constant.
• Conductance G = 1/R (in siemens, S) is the reciprocal: how easily current flows; i = Gv.
• Power follows directly: p = i²R = v²/R. These forms save you re-deriving power every time.

Kirchhoff's laws

The two conservation laws that turn a circuit into equations you can solve.

• KCL (current): the algebraic sum of currents at a node is zero, what flows in flows out.
• KVL (voltage): the algebraic sum of voltages around a loop is zero, drops equal rises.
• Watch the signs: pick a direction, and a current entering the + terminal or a drop in your travel direction is positive. Consistent signs are where most mistakes hide.

Series, parallel and division

Most networks collapse to a single equivalent by repeatedly applying two rules.

• Series resistances add (R₁ + R₂); parallel combine as product-over-sum (R₁R₂/(R₁+R₂)). Conductances do the opposite, parallel adds.
• Voltage division: a series pair splits the voltage in proportion to each resistance.
• Current division: a parallel pair splits the current in inverse proportion.

Dependent sources and checking your work

Real circuits include sources controlled by other quantities, and a tool to confirm the answer.

• A dependent source's value depends on another circuit voltage or current; the four types are VCVS, CCVS, VCCS, CCCS.
• Treat its controlling variable as an unknown and write the extra equation that defines it: that's the trick in the worked examples.
• Multisim's DC Operating Point Analysis reports every node V and branch I; solve by hand first, then let it confirm your signs and magnitudes.