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Circuit With Resistance and Capacitance Only

Author: E.E. Kimberly

In Fig. 8-7 (a) is shown a circuit containing only resistance and an uncharged condenser. If this circuit is connected to a source of alternating voltage instead of direct voltage, the current that will flow to establish dynamic equilibrium must satisfy the condition that

ee_101-9.png

The angle ϕ is the angle at which the circuit is closed after v = 0 when

ee_101-10.png

is positive.

If the condenser is initially uncharged, there is no voltage across it and it acts with no impedance. The initial current then is

ee_101-11.png

. As a< result of initial current flow, the condenser acquires a charge which produces a counter voltage. That voltage is

ee_101-12.png

The steady-state current is

ee_101-13.png

where

ee_101-14.png

The transient current is

ee_101-15.png

Therefore,

ee_101-16.png

When

ee_101-17.png

and

ee_101-18.png

By substitution of this quantity for K, we obtain:

ee_101-19.png

When

ee_101-20.png

, etc., there will be no transient component of current. Therefore, when the circuit is closed at the instant at which i89 would be a maximum, there is no transient component.

When the condenser has an initial charge, the residual condenser voltage is

ee_101-21.png

This voltage may be either positive or negative in the circuit loop and is, therefore, added algebraically to the transient voltage. From equation (8-6),

ee_101-22.png

The constant of integration K for this equation is

ee_101-23.png

and

ee_101-24.png (8-19)

The current

ee_101-25.png

is that caused by the original charge Q and is positive if the flow is around the series loop in the positive direction. It is apparent that there will be no transient current when the condenser initially is negatively charged. Hence.

When the condenser

ee_101-26.png

is initially charged, the general expression for the current is

ee_101-27.png

Example 8-5. - A circuit containing a resistance R = 5 ohms and uncharged capacitance C = 200 microfarad is connected to a 60-cycle voltage source of 70.0 volts at the instant when the voltage has reached 86.6 per cent of its maximum Value in a positive sense. Write the equation for the current.

Solution. - From equation (8-20),

ee_101-28.png



Home Electrical Transients Circuit With Resistance and Capacitance Only

Last Update: 2010-10-06