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Objective: 1. To study the behavior of capacitor in a resistor-capacitor, DC circuit. 2. Notice the current as a function of time. 3. To calculate the time constant of the given circuit. Apparatus: 1. Socket panel. 2. Resistor 1MΩ 3. Capacitor 100µF. 4. Plugs. 5. Battery. 6. Connecting wires. 7. Switch. 8. Stopwatch. 9. Ammeter. 6 8 7 3 2 4 1 5 1 Theory: The capacitor is formed of two metallic plates separated by a dielectric. The most famous example is the parallel plate capacitor. Capacitors of the same kind differ in capacitance according to the geometric shape of the capacitor. When a capacitor is connected to a DC power supply such as battery, charges build up on the plates of the capacitor and consequently the potential difference or the voltage across the plates increase until it becomes equal to the voltage of the source. The amount of charges which accumulated on the plates of the capacitor is directly proportional to the voltage across the capacitor: Q V Q CV Where: Q is the charge accumulating on the capacitor's plates, measured in C . V is the voltage drop across the capacitor, measured in V . C the proportionality constant which is called the capacitance of the capacitor, measured in F . In any charging circuit, the rate of increasing in voltage drop across the capacitor depends on the capacitance of the capacitor and the resistance in the circuit. That is true also for the discharging circuit. Therefore, the time of charging or discharging is measured in a quantity called the time constant given by: RC where R is the resistance in the circuit, measured in . The charging current in this resistor-capacitor circuit is given by: t I t I max e RC where: I t : is the current in the circuit after time t . 2 I max : is the maximum current in the circuit (i.e. at t 0 ). Studying the behavior of current during the charging process we notice that: At t 0 Q0 I 0 I max At t Q Q0 I 0 At t QQ I 0.37 I max Therefore, the time constant can be defined as the time needed, while charging, for the current to reach 0.37 of its maximum value. Circuit diagram: A Precautions: 1. Discharge the capacitor before using it. 2. Switch the key on and start the stopwatch at the same time. 3. Connect the negative plate of the capacitor to the negative terminal of the electric source. Procedure: 1. Discharge the capacitor from any residual charge. 2. Connect the circuit as in the diagram while keeping the switch off. (What does this case represent?) 3. Note the maximum current I max at t 0 . 4. Turn the switch on and start the stopwatch at the same time. 3 5. Note the current I every 0.5 min until it is coming constant and record the readings in Table (1). 6. Plot the graph of I versus t . 7. Calculate the time constant of your circuit RC . 8. Find the value of I at the time constant from the graph. 9. Calculate the ratio I I 0 . 10.Find the percentage error % for standard I I 0 0.37 . 4 Table (1) No. t min I A 1 0.0 I max 2 0.5 3 1 .0 4 1.5 5 2.0 6 2.5 7 3.0 8 3.5 9 4.0 10 4.5 11 5.0 12 5.5 13 6.0 14 6.5 15 7.0 16 7.5 17 8 .0 18 8 .5 19 9.0 20 9.5 21 10.0 I 0 5 Questions 1. What is a capacitor? What is the principle of its work? 2. Explain with graph the following: Charging a capacitor Discharging a capacitor 3. Define the time constant? Does its value change by changing the capacitor and resistor? 4. Why did you convert the time constant from s to min ? 5. Explain the reason for the following: When a lamp is connected in series with the capacitor and a DC power supply, we notice that the lamp illuminates for a short time then it will turn off. But in case of an AC power supply, the lamp will stay illuminating for long time. 6

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Charging a Capacitor, Capacitor charging, capacitor voltage, capacitor discharge, RC circuit, Capacitors in Series, high voltage, a battery, time constant, electrolytic capacitors

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views: | 107 |

posted: | 7/14/2010 |

language: | English |

pages: | 6 |

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