Kirchhoff's Laws and Electromagnetic Concepts

Kirchhoff's Loop Law

The total voltage change around a closed loop in a circuit is zero.

Equivalent Resistance (Series)

Req = R1 + R2 + R3 + ...

Equivalent Resistance (Parallel)

1/Req = 1/R1 + 1/R2 + 1/R3 + ...

Ohm's Law

V = IR

Current Calculation Example

I = 12V / 4Ω = 3A

Role of Capacitors

Capacitors can store charge when connected to a battery, and the voltage across them equals the battery's emf when fully charged.

Time Constant in RC Circuit

τ = RC, which determines how quickly a capacitor charges or discharges.

Current Change When Charging a Capacitor

I = I0 e^{-t/RC}, indicating that current decreases over time.

Voltage Change When Charging a Capacitor

VC = V(1 - e^{-t/RC})

Properties of Magnets

Magnets always have a north and south pole (dipoles), with like poles repelling and opposite poles attracting.

Compass Functionality

A compass aligns with Earth's magnetic field, pointing towards geographic north (which is actually magnetic south).

Direction of Magnetic Field Lines

Magnetic field lines go from North to South outside a magnet and South to North inside a magnet.

Finding Direction of Magnetic Field

Use the Right-Hand Rule: Thumb for direction of current, Fingers for direction of field, Palm for direction of force on positive charges.

Magnitude of Magnetic Field Around a Wire

B = μ0 I / (2 π r), where I is current and r is distance from the wire.

Force on Charged Particle in Magnetic Field

Use the Right-Hand Rule: Thumb for velocity of the charge, Fingers for magnetic field direction, Palm for direction of force (for a positive charge).

Magnetic Force on Moving Charge

F = q v B sin θ, where θ is the angle between velocity and the magnetic field.

Charged Particle Moving Parallel to Magnetic Field

It experiences no force and moves in a straight line.

Charged particle in magnetic field

It moves in a circular path due to centripetal force.

Solenoid magnetic field formula

B=μ0nIB = \\mu_0 n I B

Torque on current loop

τ=NIABsin⁡θ = N I A B \\sin \\theta

Faraday's experiments

Moving a conductor through a magnetic field creates an electric current.

Motional emf

E=vBL = v B L

Lenz's Law

The induced current in a circuit always opposes the change in magnetic flux.

Magnetic flux

ΦB=BAcos⁡θ = B A \\cos \\theta

Induced current formula

I=vBL/R = \\frac{v B L}{R}

Generator operation

A rotating loop in a magnetic field induces an emf and produces current.

Radius of charged particle's circular motion

r=mv/qB = \\frac{mv}{qB}

Centripetal force and charged particle

Because the magnetic force acts as a centripetal force, constantly pulling the particle toward the center of its circular trajectory.

Magnetic flux definition

Magnetic flux is the amount of magnetic field area lines passing through an area.

Lenz's Law direction

The direction of induced current always opposes the existing magnetic field.

Effect of increasing magnetic field strength

If magnetic field strength increases, the loop tries to induce a field in the opposite direction.

Effect of decreasing magnetic field strength

If magnetic field strength decreases, the loop tries to replace the lost field.

Charge separation in conductor

Positive charges move up, negative charges move down, causing charge separation which creates a voltage (ΔV) across the conductor.

Generator current production

Motion produces current (emf) by rotating a loop in a magnetic field, which induces a current.

What is Kirchhoff's Loop Law?

The sum of voltage changes around a closed loop is zero. (Conservation of energy)

What is the equation for Kirchhoff's Loop Law?

∑ΔV=0\sum \Delta V = 0∑ΔV=0

If you go around a loop and return to the starting point, the total voltage change is zero.