RESISTANCE AND CAPACITANCE IN SERIES 



The voltage and current waveforms are sketched in Figure 3.5. Both have the 

 same form, but not the same phase, and in fact the current through a capaci- 

 tance leads the terminal voltage by 90 degrees in an alternating current circuit. 



uuCVcosujt 



Figure 3.4 



figure 3.5 



Reactance 



The value of a resistance in ohms is given by the ratio of potential difference 

 to current; the analogous property of a capacitance is also measured in 

 ohms and is called the capacitive reactance, symbol X^. Numerically it 

 equals VJimCV) — IjiojC), the phase difference represented by the sine and 

 cosine terms being ignored. Capacitive reactance is conventionally regarded 

 as being negative in sign, for a reason which appears in Chapter 5. 



Power in capacitances 

 In Figure 3.4 the instantaneous power supphed to the capacitance is 



P= vi 



= Fsin cot . coCV cos cot 



= V^Cco sin cot . cos cot 



= ^V^Cojsinlcot 



This function moves positive and negative symmetrically, which means 

 that power surges back and forth into the capacitance and out again. On the 

 average the power supplied is 



iV^Cco 



1 n^ 



2-n- Jo 



sin 2cot dt = 



Therefore, no power is consumed by a capacitance. 



1/4 



figure 3.6 



RESISTANCE AND CAPACITANCE IN SERIES 



Series R and C connected to a constant direct current generator 



If a resistance and a capacitance are connected in series to a generator of 

 constant direct current / {Figure 5.(5), upon opening the switch a waveform is 



27 



