RESISTANCES AND CAPACITANCES 



then, rationalizing, 



^ -jXcR{R+jXa) 



R' + Xc' 

 Xc'R-jR^Xa 



~ R^+ Xc^ 



This, however, is the impedance of a series combination, comprising 

 a resistance of {Xq^R)j{^ + X(j^) and a capacitance of reactance 

 (R^Xc)l(R^ + A'c^). The phase angle is thus seen to be 



tan" 



R^X, 



c 



Xc'R'^^"" Xc 



Summarizing, then, the two networks in Figure 3.39 are equivalent at one 



R 



HT}- 



Impedance 



RX, 



r/?2*x2y/2 



Phase angle r tan" ' Ft 



-|| — V\AAA-o 



Impedance Is (r2+ x2)'/2 

 Phase angle = tan"' '^c 



frequency, that at which 



R^Xr 



Figure 3.39 



^C D2 \_ V 2 



R' + Xc' 



and 



r = 



Xc'^R 



R' + Xc^ 



Potentiometer feeding a piece of screened cable 



R-C filters are not always built into apparatus by design ; they sometimes 

 occur unintentionally. For example, in Figure 3.40, a piece of apparatus A 



B 



Figure 3.40 



is supposed to be feeding another piece of apparatus B via a length of screened 

 cable. P is an amphtude control, a potentiometer to adjust the quantity of 

 signal transferred from AXo B\ the load imposed on /I by 5 is assumed to 

 be negligible. 



42 



