C4 Charging and Discharging of a Capacitor

C4 Charging and Discharging of a Capacitor - CHARGING AND...

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CHARGING AND DISCHARGING OF A CAPACITOR INTRODUCTION In this experiment, we will study charging a capacitor by connecting it to a voltage source through a resistor. The experiment also includes the study of discharging the capacitor through a resistor. OBJECTIVES: To study the charging and discharging processes of capacitors. To determine the time constant τ of an RC-circuit. EQUIPMENT TO BE USED: ~200 k resistors. 2 ~330 μ F capacitor. 1 Xplorer GLX 1 Multimeter. 1 Voltage sensor CI6685 1 Alligator clip leads 4 10 V supply 1
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THEORY: Charging a Capacitor: Consider a circuit as shown in Figure 1. Capacitor ܥ is initially uncharged. By closing the switch ܵ , a current ݅ is set up in the loop and the capacitor begins to charge. Applying Kircho f’ s loop rule, we get ܧെܴ݅െ ܳ ܥ ൌ0 (1) where ܧ is the supply voltage, ܴ is the resistance, ܳ is the charge on the capacitor and ܥ is the capacitance. Substituting for the current ݅ uatio (1) becomes , Eq n ܧെ ݀ܳ ݀ݐ ܴെ ܳ ܥ (2) Figure 1: Charging circuit Rearranging the terms, Equation (2) bec s ome ݀ܳ ݀ݐ ܧ ܴ ܳ ܴܥ (3) The solution of Equation (3) is given as ܳൌܥܧ ൬1െ݁ ି ோ஼ (4) which determines the charge on the capacitor as a function of time ݐ . ܥܧ ൌ ܳ ݋ represents the maximum charge the capacitor can hold for a given voltage. The voltage across the capacitor ܸ is given as
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ܸ ܳ ܥ (5) Dividing Equation (4) by ܥ yields ܸ ൌܧ ൬1െ݁ ି ோ஼ (6) At a speci c value of time ݐൌ߬ൌܴܥ nstant of the R-C circuit), (called the time co ܸ ൌܧሺ1െ݁ ିଵ (7) ܸ ൌ 0.63ܧ (8) Therefore, by plotting ܸ versus ݐ , the time constant ߬ may be determined, and hence, the value of ܥ can be calculated, provided ܴ is known. Equation (6) shows that the growth of the capacitor’s voltage is not linear, but rather grows exponentially reaching a saturation value which equals the voltage of the voltage source. The capacitor is considered to be fully charged after a period of about ve time constants. The current ݅ in the circuit at a given time ݐ is g n a ive s ݅ൌ ݀ܳ ݀ݐ ܧ ܴ ݁ ି ோ஼ (9) where ൌ݅ represents the initial current in the circuit. Therefore we can write ݅ൌ݅ ݁ ି ோ஼ (10) At time ݐൌ߬ , ݁ ିଵ ൌ 0.37݅ Discharging a Capacitor: For the discharging process, consider the circuit shown in Figure 2. After closing the switch ܵ for a long time (compared to the circuit’s time constant), the capacitor will be fully charged to a
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C4 Charging and Discharging of a Capacitor - CHARGING AND...

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