By G. H. Olsen (Auth.)
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Additional resources for Electronics. A Course Book for Students
Vc + VR = 0 Let us see how the equations and the term 'time constant' arise. V = Vr + V = iR + c fiat ßc Since V, the supply voltage, is a constant, differentiation yields 0 = Κ-4^- + 4 γ di C Separating the variables and integrating J Therefore l o g e / = CR fdi_= i _ J fàL CR h k (the constant of integration). A t time t = 0 the capacitor is uncharged, therefore the voltage across the capacitor terminals is zero. All of the supply voltage, therefore, appears across R hence V = IR at time t = 0 (where / is the value of i at zero time).
When q is in coulombs and V in volts, C is in farads. The farad, F, is a very large unit of capacitance for electronic purposes so the microfarad, μ¥, which is one millionth of a farad, is used. The picofarad (pF) is one millionth 6 12 of a microfarad so l p F = 10~ μΡ = 10" F. Since V Ë ? e. q = CV cdt We have already seen that dq/dt (a rate of change of charge with time) is the current flowing, therefore . dV r ι = C— di The simple Ohm's Law relationship for resistors cannot therefore be applied to capacitors since the current is proportional not to the applied voltage, but to the rate of change of the voltage.
Is rising or falling, therefore, the inductor opposes changes of current in the circuit. f. increases. In a sense, the inductor may be said to have 'electrical inertia'. f. f. and i the instantaneous value of the current. Hence Tdi e = -L— at where L is the constant of porportionality known as the selfinductance of the coil. When i is in amperes, t is in seconds and e is in volts, L is in henries (H). f. produced is I V . Like the capacitor, no simple relationship exists between the applied voltage and the current; the implications of this are discussed in Chapter 3.
Electronics. A Course Book for Students by G. H. Olsen (Auth.)