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Chapter 4 - Chapter 4 TRANSIENTS 4.1 First-Order RC...

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Chapter 4 TRANSIENTS 4.1 First-Order RC circuits Discharge of a Capacitance through a Resistance Figure 4.1 shows a fluid flow analogy of a capacitor discharging. Cutting to the chase, the formula for voltage as a function of time when a capacitor is discharging is ( ) t RC C initial v t V e - = . RC is called the time constant for obvious reasons. At one time constant, the voltage across a capacitance discharging through a resistance is 1 0.368 e - 2245 times its initial value. After about three to five time constants, the capacitance is almost totally discharged. Show figure 4.2 Charging a Capacitance from a DC Source through a Resistance When a dc source is connected in an RC circuit, the total response contains two parts; forced (or steady-state) and transient. Figure 4.3 shows a capacitance charging through a resistance. The switch closes at t=0 connecting the dc source V S to the circuit. At t=0 the voltage across the capacitance equals zero. Show figure 4.3 and overlay 4.4. The formula for voltage across a capacitor that is in series with a source V S and a resistor R is as follows: 1 ( ) RC C S S v t V V e - = - As with discharging, the charging rate is 63.2% for each time constant. Exercise 4.1 Suppose R=5000Ω and C=1μF in 4.1a. Find the time in which the voltage across the capacitor reaches 1% of its initial value.

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Chapter 4 - Chapter 4 TRANSIENTS 4.1 First-Order RC...

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