Current Electricity

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Electric current is the net amount of charge flowing across a cross-section per unit time. It is defined as I = Q/t, where Q is charge and t is time. The SI unit is ampere (A). For varying current: I(…

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Ohm's Law states that the potential difference (V) across a conductor is directly proportional to the current (I) flowing through it, provided temperature and other physical conditions remain constant…

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Resistance is directly proportional to length (l) and inversely proportional to cross-sectional area (A): R = ρl/A, where ρ is resistivity. When length doubles, resistance doubles (R ∝ l). When area h…

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Resistivity (ρ) is a material property that opposes current flow, with SI unit Ω⋅m. It's given by ρ = RA/l. Conductivity (σ) is the reciprocal of resistivity: σ = 1/ρ, with SI unit S/m (siemens per me…

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Drift velocity (vd) is the average velocity of charge carriers in a conductor under an electric field. For current: I = nAevd, where n is number density of charge carriers, A is cross-sectional area, …

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Under electric field E, electrons experience acceleration a = -eE/m. After average collision time τ, drift velocity is: vd = -eEτ/m. The magnitude is |vd| = eEτ/m. This shows drift velocity is proport…

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Mobility (μ) is the magnitude of drift velocity per unit electric field: μ = |vd|/E. From drift velocity formula: μ = eτ/m, where τ is relaxation time and m is mass of charge carrier. SI unit is m²/(V…

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From j = nevd and vd = eEτ/m, we get j = (ne²τ/m)E. Comparing with j = σE, conductivity is: σ = ne²τ/m. Since ρ = 1/σ, resistivity is: ρ = m/(ne²τ). This connects macroscopic properties to microscopic…