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Unformatted text preview: q q = = Q Q cos( cos( ϖ t t + + φ ) ) and q is the charge on the capacitor. and q is the charge on the capacitor. where ω LC 1 = Energy in LC circuits 2 2 2 cos ( ) 2 2 E q Q U t C C ϖ φ = = + 2 2 2 1 1 2 2 sin ( ) B U Li LI t = = + constant B E U U U + = = 2 2 max max 2 2 E B Q LI U U C = = = Energy oscillation in LC circuit Energy vs time when the current is a maximum at t=0.0.2 0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2 Time in Periods Ratio of U E to U B U = U B + U E U B U E t = /8 t T = / 4 t T = 3 /8 t T = 5 / 2 t T = 4 3 2 1 6 5 /8 t T = 3 / 4 t T = 7 /8 t T = 7 8 1 2 3 4 5 6 7 8 Energy oscillation in an LC circuit 1 Writing the loop equation for emf: 2 2 1 d q dq L R q dt dt C + + = This is the equation for the motion of damped harmonic oscillator, with solution: ( 29 / ( ) cos ' t q t Qe t τ ϖ φ= + 2 L R τ= 2 1 1 ' LC =with: and RLC Circuit...
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 Spring '07
 Schroeder
 Energy, dt, RC circuit, RL circuit, LC circuit

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