Unformatted text preview: RC time constant is τ = RC 8.4.2 Discharging a Capacitor If we move the switch in ﬁgure 25 to position b and repeat our analysis, we ﬁnd R dq dt + q C = 0 The solution to this homogeneous linear diﬀerential equation is q = q e-t RC ⇒ i =-± q RC ² e-t RC So, we see that discharging a capacitor also has an exponential time dependence with the same characteristic time constant. 8.5 Problems Problem 27.33 In ﬁgure 26 the ideal batteries have emfs E 1 = 5 V and E 2 = 12 V , the resistances are each 2Ω, and the potential is deﬁned to be zero at the grounded point of the circuit. What are potentials (a) V 1 and (b) V 2 at the indicated points? The ﬁrst step in this problem is to simplify the two resistors in the upper right corner of the circuit. Since they are in parallel their equivalent resistance is P 1 = 1 1 R + 1 R = R 2 31...
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- Spring '08
- Physics, RC circuit, Electrical resistance, τ, RC time constant