Week 1: Ohm's Law, DC Circuits

What is Ohm’s Law, and how is it expressed mathematically?

• Ohm’s Law states that the voltage across a resistor is proportional to the current through it. It is expressed as V=IR, where V: voltage, I: current, R: resistance.

How is the voltage drop across a resistor calculated, and what does it depend on?

ΔVR=IR. It depends on the current through the resistor and its resistance.

How do you calculate the equivalent resistance for resistors in series?

R_eq = R₁ + R₂ …

How do you calculate the equivalent resistance for resistors in parallel?

1/R_eq = 1/R₁ + 1/R₂ …

What is Kirchhoff’s Junction Law, and what physical principle does it represent?

States that the sum of currents entering a junction equals the sum of currents leaving it. It represents the conservation of electric charge.

What is Kirchhoff’s Loop Law, and how is it applied?

States that the sum of voltage changes around a closed loop is zero. It is applied by summing all voltage drops and rises around a circuit loop.

How is the voltage across a capacitor calculated?

The voltage is V_C= q/C, where q: charge on the capacitor, C: capacitance.

How do you find the current through a resistor in a simple circuit?

Use Ohm’s Law and rearrange to I = V/R

How do you apply Kirchhoff’s laws to solve multi-loop circuits?

• Use Junction Law to write equations for current conservation at nodes.

• Use Loop Law to write equations for voltage conservation around each loop.

• Solve the resulting system of equations for currents.

How do you find the equivalent resistance in a complex circuit with series and parallel resistors?

Combine resistors in series and parallel step-by-step, simplifying the circuit until a single equivalent resistance remains.