University:
Kentucky State University
Course:
PHY 212 | General Physics II
Academic year:

2024
Views:

120

Pages:

21
Author:

gryzli155

CH.25: Capacitance: Capacitor: Two isolated conductors. Used to store electric field. Types of Capacitor: * Two parallel plate capacitor * Cylindrical capacitor * Spherical capacitor C = Q/V [C] = [Q]/[V] = C/V = farad = F Note: Capacitance depends only on geometrical + the medium. Parallel plate capacitor C = Q/ΔV Gaussian surfaces ∫E.dA = q_inc EA = q/ε₀ E = q/ε₀A ΔV = ∫E.ds = ∫Edx = Ed ΔV = Ed C = Q/ΔV = ε₀AE/Ed = ε₀A/d C = ε₀A/d P1 Page 677 Ceq = ? C1 = 10 mF C2 = 5 mF C3 = 4 mF Sol: C1, C2 in parallel C12 = C1 + C2 = 10mF + 5mF = 15 mF Ceq = C12 in series 1/Ceq = 1/C12 + 1/C3 = 1/15 + 1/4 = 19/60 => Ceq = 60/19 mF Energy stored in Capacitor: The work done by an external agent: ΔV = -W/Q Assume dq dW = ΔVdq ∫dW = ∫(q/C)dq Wₐ = 1/2(q²/C) ⇒ Wₑ = -Wₐ = -q²/2C Wₑ = -U_(capacitor) = -Wₐ Wₑ = U_(capacitor) = -Wₐ Wₐ = U_(capacitor) U = 1/2(q²/C) energy stored in the capacitor. = 1/2(1/C)C²V² = 1/2(q/V)V² U = 1/2CV² U = 1/2QV Note: Capacitance 'C' is constant (geometrical shape & medium) Electric Energy of the Capacitor: | - | | C = Q/V₀ U = 1/2 CV₀² | - | | Q = 2Q₀ C = C₀ U = 1/2 C₀(2V₀)² = 4U₀ Energy Stored in Capacitor: U = 1/2 Q²/C = 1/2 CV² = 1/2QV