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PH 122 (46)

Capacitor formulas, capacitors in series and in parallel, capacitor discharge, exponential decay

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PH 122
Brian Jones

19 February Capacitor formulas Charge on a capacitor with potential difference ΔC Q = C ΔV C Unit: farad, F; 1 farad = 1 F = 1 C/V Capacitance of a parallel-plate capacitor with plate area A, separation d ε0A C = d Capacitance of a parallel-plate capacitor with a dielectric of dielectric constant κ κε A 0 C = d Capacitors in series and in parallel Equivalent capacitance of N parallel capacitors C eqC +1C + 2 + …3+ C N Equivalent capacitance of N series capacitors 1 1 1 1 + + +⋯+ C eq( C 1 C 2 C3 C N ¿¿−1 Capacitor Discharge τ = RC −t τ ΔV C (ΔV )C 0 e After 1 time constant, voltage decayed 37%. Exponential decay Exponential decay occurs when a quantity y is proportional to the number e taken to the power –t/τ. The quantity τ is known as the time constant. We write this mathematically as −t y = A e τ Whenever t increases by one time constant, y decreases by a factor of 1/e. For instance At time t = 0, y = A. Increasing time to t = τ reduces y to A/
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