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ECE3183 Exercises in capacitances and inductances Version 1.4 C-1. The conceptual capacitance is shown by the figure. A typical high-voltage capacitance is a foil wrapped glass plate (relative dielectric constant K = 3.9). For a plate that is 2mm thick and has dimensions 20cm x 30cm (about the size of a sheet of notebook paper), determine (a) capacitance between the top and bottom foils. (b) If a voltage of 2000V is applied between the top and bottom foil, how much charge is accumulated in µC? (c) How much energy does this represent (in µJ)? (d) If the charge is released in 2 µs, how much current flows? C-2. Determine equivalent capacitance Ceq for each of the following capacitances by inspection. C-3. Determine designated voltages by inspection. C-4. For problem C-3 determine (1) the energy stored across each capacitance for which you determined voltage and (2) the energy stored by the equivalent capacitance of the network. C-5. Determine (1) the value of voltage Vo after the switch is closed. (2) the total energy stored on the capacitances before the switch is closed (3) the total energy stored on the capacitances after the switch is closed. C-6. For each of the following RC series combinations determine time-constant τ by inspection (a) R = 1kΩ, C = 2µF τ = ___________ (b) R = 100kΩ, C = 4µF τ = ___________ (c) R = 50kΩ, C = 4pF τ = ___________ (c) R = 200Ω, C = 20pF τ = ___________ (e) R = 2MΩ, C = 4pF τ = ___________ (f) R = 2.5MΩ, C = 12fF τ = ___________ C-7 For each of the following RL series combinations determine the time constant τ by inspection (a) R = 1kΩ, L = 2µH τ = ___________ (b) R = 100Ω, L = 5mH τ = ___________ (c) R = 50kΩ, L = 2mH τ = ___________ (c) R = 200Ω, L = 20µH τ = ___________ (e) R = 2MΩ, L = 4µH τ = ___________ (f) R = 2.5MΩ, L = 2mH τ = ___________ C-8. For each of the following circuits determine v(0), v( ∞ ) time constant τ, and the behavior v(t) as the circuit relaxes C-9. For each of the following RL series combinations determine time-constant τ by inspection (a) R = 1kΩ, L = 2µH τ = ___________ (b) R = 100kΩ, L = 4µH τ = ___________ (c) R = 50kΩ, L = 4mH τ = ___________ (c) R = 200Ω, L = .02µH τ = ___________ (e) R = 2MΩ, L = 4nH τ = ___________ (f) R = 2.5MΩ, L = 12nH τ = ___________ C-10. For each of the following circuits determine (1) the complex impedance (2) the phasor form of the impedance (3) the complex admittance C-11. For the circuits of problem C-10 determine the frequency (in both rad/sec and Hz) at which the real and imaginary parts of the impedance (or admittance) are equal.