. Electronic apparatus for biological research. Electronic apparatus and appliances; Biology -- Research. RESISTANCES AND CAPACITANCES by the scalar IR, the product is a directed quantity {Figure ). Similarly when sin Mt is multiphed by the scalar —IjcoC the product is another directed quantity (downward, because capacitive reactance is by convention negative) {Figure ). Their sum is obtained by vector addition {Figure ). The Yf^ of length//? IR Figure I/cuc. V(,, of length Figure Figure angle between y^ and y^^ is the phase angle ^, which is now seen to be equal to
. Electronic apparatus for biological research. Electronic apparatus and appliances; Biology -- Research. RESISTANCES AND CAPACITANCES by the scalar IR, the product is a directed quantity {Figure ). Similarly when sin Mt is multiphed by the scalar —IjcoC the product is another directed quantity (downward, because capacitive reactance is by convention negative) {Figure ). Their sum is obtained by vector addition {Figure ). The Yf^ of length//? IR Figure I/cuc. V(,, of length Figure Figure angle between y^ and y^^ is the phase angle ^, which is now seen to be equal to tan -1 ^/^ = tan-i 1 IR mCR and the length of t;^^, which gives us [y^^l, is now seen by Pythagoras to be \{IRf + \o)c) 2U/2 i\r^ + 2U/2 Thus the complete description of y^^ is modulus phase angle Y 'AB { i 1 \2U/2 i 1 / W + 1^1 j cos(w? + ^) where ^ - tan-i ^j^^ Impedance—The impedance of the circuit is the ratio of terminal voltage to current, is measured in ohms, and is symbohzed by Z. It expresses with circuits containing resistances and capacitances the amount of opposition to the flow of current, in a manner analogous to the notions of resistance and reactance in circuits containing, respectively, resistors and capacitors only. The presence of the phase difference between voltage and current makes impedance a 'complex number', containing a modulus part and an angle part. If, for the present, we restrict ourselves to the modulus, then \vj^j,\=I\Z\ {) and on comparing this with the expression for y^^ above or, remembering that capacitive reactance, X^ = lIcoC \z\ = {R' + {Xc)'yi^ The network we have been discussing is an extremely simple one, yet the analysis has yielded a square root term, and square root terms are notoriously tiresome in calculations. It is not hard to see that in the analysis of more elaborate resistance and capacitance networks, the equations are liable to become very unwieldy. There is an analytical technique which we shall use 32. Please no
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