# Termination in Inductance and Capacitance

## Shunt Capacitance

Using the Thevenin equivalent circuit as shown in Figure 10.22, the voltage rise across the capacitor C is v_{C} *=* 2v;( 1 — *e*^{—t}=^{Z0C}), where t is the time commencing with the arrival of the wave at C. The current through C is given by,

**Figure 10.22 **Termination of line (surge impedance Zo) in a capacitor C or inductance L

The reflected wave,

When *t =* 0, *v _{C} =* 0 and i = 2vi/Zo and when

*t*! 1, v

_{C}

*= 2v{*and i = 0. That is, as to be expected, the capacitor acts initially as a short circuit and finally as an open circuit.

## Shunt Inductance

Again, from the equivalent circuit shown in Figure 10.22 but with an inductor the voltage across the inductance is

and

Here, the inductance acts initially as an open circuit and finally as a short circuit.

## Capacitance and Resistance in Parallel

Consider the practical system shown in Figure 10.23(a), where C is used to modify the surge.

**Figure 10.23 **Two lines surge impedances Z**1** and Z**2** grounded at their junction through a capacitor C. (a) System diagram, (b) Equivalent circuit

From Figure 10.23(b), the open-circuit voltage across AB without the capacitor:

Equivalent Thevenin resistance = —^{1}—^{2 }Voltage across AB is ^{1} ^ ^{2}

)

The reflected wave is given by (v_{AB} — v).

Example 10.2

An overhead line of surge impedance 500 V is connected to a cable of surge impedance 50 V through a series resistor (Figure 10.24(a)). Determine the magnitude of the resistor such that it absorbs maximum energy from a surge originating on the overhead line and travelling into the cable.

Calculate:

a. the voltage and current transients reflected back into the line, and

b. those transmitted into the cable, in terms of the incident surge voltage;

c. the energies reflected back into the line and absorbed by the resistor.

**Answer:**

Let the incident voltage and current be * vi* and

*, respectively. From the equivalent circuit (Figure 10.24(b)),*

**ii**

As * v_{i}* = —

_{1}

**ii,**

Power absorbed by the resistance This power is a maximum when

**Figure 10.24 **(a) System for Example 10.2. (b) Equivalent circuit, (c) Voltage and current surges

With this resistance the maximum energy is absorbed from the surge. Hence R should be 500 + 50 = 550 V.

a. the reflected voltage at A

And

b. Voltage and current transmitted into the cable

c. The surge energy entering Z_{2} = * v_{B}i_{B} — 0.082v_{i}i_{i }*The energy absorbed by

*— (0.91i*

**R**_{i})

^{2}x 550

and the energy reflected — * v_{i}i_{i}(1 —* 0.082 — 0.91) — 0.008v,-ii The waveforms are shown in Figure 10.24(c).