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# Consider a circuit having a 30-volt source, switch, resistance R, capacitor 0.01 microfarad, and resistance 10 kiloOHM connected in series?

Consider a circuit having a 30-volt source, switch, resistance R, capacitor 0.01 microfarad, and resistance 10 kiloOHM connected in series when the switch in this circuit is closed. The voltage across the capacitor must rise to 6.59 volt in 0.1 ms.

Identify the value of R that should be used.

### 2 Answers

- oubaasLv 72 months agoFavorite Answer
1-6.59/30 = e^-K

0.780 = e^-k

k = -ln 0.780

k = 0.25 = t/T

T = t/k = 10^-4/0.25 = 4*10^-4 sec = R'*C

R' = T/C = 4*10^-4*10^8 = 4*10^4 ohm

R = R'-10^4 = 3*10^4 ohm (30 kohm)

- billrussell42Lv 72 months ago
v = v₀[1–e^(–t/τ)]

6.59 = 30[1–e^(–0.0001/τ)]

6.59 = 30[1–e^(–0.0001/τ)]

1–e^(–0.0001/τ) = 0.2197

e^(–0.0001/τ) = 0.7803

–0.0001/τ = ln(0.7803) = –0.2481

τ = 0.0001/0.2481 = 0.0004031 s

RC = τ = 0.0004031

R = 0.0004031/0.01e-6 = 40310 Ω

added R = 40310 – 10000 = 30310 Ω

voltage on a cap, charging

v = v₀[1–e^(–t/τ)]

v₀ is the battery voltage

v is the voltage after time t

R is resistance in ohms,

C is capacitance in farads

t is time in seconds

RC = τ = time constant