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RC01-21-2011

# RC01-21-2011 - HB MS RC Circuits(1 1 RC Circuits Equipment...

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HB, MS 01-21-2011 RC Circuits (1) 1 RC Circuits Equipment SWS with 750 interface, RLC circuit board, 2 voltage sensors (no alligator clips), 2x35 in. leads, 12 in. lead Reading Review operation of SWS oscilloscope. Review operation of the SWS signal generator. 1 Introduction The 3 basic linear circuits elements are the resistor, the capacitor, and the inductor. The voltage across a resistor is proportional to the current through the resistor. The voltage across a capacitor is proportional to the time integral of the current into the capacitor. The voltage across an inductor is proportional to the time derivative of the current through the inductor. This lab is concerned with the characteristics of capacitors and circuits consisting of a resistor and a capacitor in series (RC circuits). The primary focus will be on the response of an RC circuit to a step voltage and a voltage square wave. (A step voltage is a constant voltage which instantaneously changes to a diﬀerent constant voltage.) 2 Capacitors A capacitor is a 2 terminal circuit element that stores energy in its electric ﬁeld. In its simplest form a capacitor consists of 2 parallel plates separated by a small gap which is usually ﬁlled with a non-conducting dielectric material. In practice many capacitors are made by sandwiching a dielectric sheet such as mylar between 2 pieces of metal foil and rolling this assmebly up into a cylinder. If a positive current I enters one plate of a capacitor and exits the other plate a positive charge Q builds up on the ﬁrst plate and a negative charge -Q builds up on the second plate. A voltage V C developes across the capacitor. The charge Q and voltage V C are linearly related by the equation Q = CV C , (1) where C is a constant called the capacitance. Eq. 1 can also be written as V C = 1 C Z Idt. (2) The unit of capacitance in S.I. units is the farad (F). One farad is a huge capacitance and more usual units are the micro farad ( μ F) and the pico farad (pF). The constant C depends on the geometry of the capacitor and the dielectric properties of the insulator between the plates. The most important speciﬁcation for a capacitor of a given value is its maximum voltage rating. 3 RC Circuits A series RC circuit with a voltage source V(t) connected across it is shown in Fig. 1. The voltage across the resistor and capacitor are designated by V R and V C , and the current

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HB, MS 01-21-2011 RC Circuits (1) 2 around the loop by I. The signs are chosen in the conventional way. I is positive if it is in the direction of the arrow. Kirchoﬀ’s law, which says that the voltage changes around the loop are zero, may be written V R + V C = V. (3) Letting V R = IR = ( d dt Q ) R and V C = 1 C Q Eq.(3) may be written as R d dt Q + 1 C Q = V. (4) Of particular interest in this lab is the solution of Eq.(4) when
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RC01-21-2011 - HB MS RC Circuits(1 1 RC Circuits Equipment...

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