The average translational kinetic energy of gas molecules is directly proportional to absolute temperature: $\langle K \rangle = \frac{3}{2}k_B T = \frac{3}{2} \frac{R}{N_A} T$ Where:

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The distribution of molecular speeds in a gas follows the Maxwell-Boltzmann distribution: $f(v) = 4\pi \left(\frac{m}{2\pi k_B T}\right)^{3/2} v^2 e^{-mv^2/(2k_B T)}$ Key features:

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Electric charge is conserved in all physical processes.

• Total electric charge in an isolated system remains constant
• Charge cannot be created or destroyed, only transferred

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The electrostatic force between two point charges: $F = k\frac{|q_1||q_2|}{r^2}$ Vector form:

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Electric current is the rate of charge flow: $I = \frac{dq}{dt}$ Units: Amperes (A) = C/s

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Resistance: opposition to current flow $R = \frac{V}{I}$ Units: Ohms (Ω) = V/A

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Kirchhoff's Junction Rule (Current Law): Sum of currents entering junction equals sum leaving: $\sum I_{in} = \sum I_{out}$

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represent magnetic field direction and strength. Properties:

• Form closed loops (no beginning/end)

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RC Circuits Steady State: Steady state after long time ($t \gg \tau$):

• Capacitor fully charged

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Angle of incidence equals angle of reflection: $\theta_i = \theta_r$ All angles measured from normal (perpendicular to surface)

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Transverse waves:

• Particle motion perpendicular to wave propagation
• Examples: waves on string, electromagnetic waves

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• Amplitude (A): maximum displacement from equilibrium
• Wavelength (λ): distance between successive identical points (crest to crest)
• Frequency (f): number of complete cycles per second (Hz)

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Planck-Einstein relation for photon energy: $E = hf = \frac{hc}{\lambda}$ Where:

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Emission of electrons when light strikes metal surface. Einstein's photoelectric equation: $K_{max} = hf - \phi$

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