Shortcut Methods and Tricks

• Using Ohms’s Law: The current flowing through a conductor is directly proportional to the voltage applied across its ends and inversely proportional to its resistance. This can be expressed as:

$$ I = {V \over R} $$

where I is the current, V is the voltage, and R is the resistance.

• Using Series and Parallel Resistors:

• In a series circuit, the total resistance is the sum of the individual resistances.

• In a parallel circuit, the total resistance is given by: $$ {1 \over R_{total } } = {1 \over R_1 } + {1 \over R_2 } +…$$

• Kirchhoff’s Loop Rule: In a closed loop, the algebraic sum of the voltages around the loop must equal zero. This rule can be used to find the unknown voltage or current in a circuit.

• Kirchhoff’s Junction Rule: At any junction in a circuit, the algebraic sum of the currents entering the junction must equal the algebraic sum of the currents leaving the junction. This rule can be used to find the unknown current in a circuit.

• Thevenin’s Theorem: This theorem enables one to find the equivalent circuit for any DC circuit that drives an output through two terminals. To find the Thevenin equivalent circuit for a circuit, two steps must be done:

• Open the circuit at the terminals for which the Thevenin equivalent is being sought.

• From the created open-circuit, calculate the voltage across the open terminals (Vth).

• Short-circuit the open terminals again.

• Measure the short-circuit current (Ith).

• Find the Thevenin resistance (Rth), using: $$ R_{th} = {V_{th} \over I_{th} } $$

• Norton’s Theorem: Like Thevenin’s theorem but, in this case, the equivalent circuit is built with a constant current source in parallel with a resistance instead of a voltage source in series with a resistance.