Experiment 3 Capacitance A bridge circuit is used to determine the capacitance o

Question

Experiment 3 Capacitance A bridge circuit is used to determine the capacitance of a parallel plate capacitor. Once the capacitance is found, the dielectric constant of the material separating the plates is subsequently determined. Theory Bridge circuits are designed to allow the determmation of the value ofan unknown cincuit element such as a resistor, capacitor, or an inductor. The circuit diagram for a typ bridge is shown in Figure 1 The bridge elements are comected between junctions AC, BC, AD, and BD V represents either an AC or DC voltage source and G represents a null detecting device such as a galvanometer, a voltmeter, or an oscilloscope. Generally, one or more of the circuit elements in the bridge can be varied until the potential difference between junctions A and B (V AR) is zero. When this situation exists. the bridge is said to be balanced or is "nulled." The following relationships then hold for the voltages Figure 1. A typical bridge circuit. in the main branches:- AC (20 of the remainng three. For example, the voltage between junctions A and D isy (3) AC

Explanation / Answer

* The main error because of the limiting errors of the three unknown resistances.hence very persistances are required having tolerance of 1% or even 0.1%.
There are also possible indeterminate errors:
(1) Insufficient sensitivity of the galvanometer.
(2) Non-uniformity of the slidewire.
(1) Insufficient sensitivity of the galvanometer:
There are mainly two effects of current, such as heating effect and magnetic effect. Each and every utilization of electricity, we see in our daily life, is either due to heating effect or due to magnetic effect of current. For examples, the light bulb glows in our house is due to heating effect of current and the fan rotates in our house is due to magnetic effect of current. There are thousands of other examples which can illustrate the effect of current, too.
Heating Effect :
Whenever current passes through a conductor there would be a generation of heat due to ohmic loss in the conductor. This is commonly known as heating effect of current.
when the current passes through the resistances, due to the heating effect (i square r) the temprature increases.hence the values of the resistances of the bridge arms changed due to heating effect.
Since, we cannot use electric power directly, we need to convert it into another usable power, like heat, light, or mechanical power etc. When current flows through a conductor some loss occurs and this loss is almost inevitable, and more the resistance of the conductor, more the loss. This loss due to the electrical resistance of conductor is mainly responsible for the heating effect of current.
As some electric power is converted into heat energy, this phenomenon can be described by Joule's law, which states that,
Where, H is the generated heat in calories, i is the current that is flowing through the wire and it is measured in amperes, r is the resistance of the conductor in ohm() and t is the duration of current flowing in seconds. If we know the time of current flowing, the resistance of wire, and amount of current flow, we can easily find out the generated heat of the circuit. This heat can be utilized in various ways.
We saw that the more the electrical resistance of the wire the more the generated heat in the circuit, but to know more accurately about the heating effect of current, we should know about it from the atomic level. As the flow of current is nothing but the flow of electrons there will always be resistance from the fixed atoms of the conductor. The fixed atoms of the wire resist the flow of electrons and as a result there are collisions and as the kinetic energy converts into heat energy we see that the wire is getting hot.
Applications of Heating Effect:
Now, the generated heat can be viewed from many points of angles. Sometimes, it is only seen as a loss and is trying to be minimized. Various steps are taken to minimize heat dissipation from the conductor. But we can see many positive applications of heating effect of current in our daily life. Electric iron, the whole idea or working principle depends upon the heating effect of current. High resistant wire is used as the main coil in the electric iron when current flows through the coil, the coil gets heated and the iron works. But what about over heating of electric iron? This problem can be solved by using bimetallic conductors. Bimetallic plates made of two different metals are used in the circuit. As expansion co-efficient of heat is different for two metals, so due to heating effect one metal's expansion is different from the other metal; as a result the plate is bent and after reaching at a certain temperature the contact of the circuit is broken and current flowing through the coil is stopped and the electric iron too is not heated any more.
The same mechanism is used in electric heater, the only difference is that there is no bimetallic plate or circuit breaker involved.
Another application of heating effect of current is seen in electric bulbs. The wire which is used inside the bulb gets illuminated and emits light after reaching certain temperature. The metal used in the bulb is mainly made of tungsten.
Finally and perhaps the most important application of the heating effect of current is in electrical fuses, that are used in almost everywhere. From huge industries to domestic level, everywhere electrical fuse is a must. The fuse is made of such metals which has a certain melting point. They are okay for normal current but when over current flows through the circuit; the generated heat in the fuse wire is enough to melt the metal portion of the fuse wire and break the circuit. In this way the costly equipment is protected as huge current flow, can damage the equipment permanently.
Thermal e.m.f:
In the galvonometer circuit the dissimilar metals comes in contact and generate the thermal emfs.such thermal e.m.f.s may cause the errors while measuring the low resistances values.To prevent this more sensetive ,galvonameter having copper coils and copper suspenstion systems are used.
(2) Non-uniformity of the slidewire:
The nonlinearity error occurs because, when strain measurements
are made with an “unbalanced” Wheatstone
bridge circuit (as described in Section 2.0), there are certain
conditions under which the output of the bridge circuit is
a nonlinear function of the resistance change(s) producing
that output. The error due to the nonlinearity, when
present, is ordinarily small, and can usually be ignored
when measuring elastic strains in metals. However, the
percentage error increases with the magnitude of the strain
being measured, and can become quite significant at large
strains (for example, the error is about 0.1% at 1000, 1%
at 10 000, and 10% at 100 000; or, as a convenient rule
of thumb, the error, in percent, is approximately equal to
the strain, in percent).
Most static strain indicators and signal conditioners
for use with resistance strain gages use a form of the
Wheatstone bridge circuit in which the bridge arms consist
of one to four active gages. The classical Wheatstone
bridge arrangement has been used for many years for the
accurate measurement of a single unknown resistance;and, in such instruments, the bridge is balanced at the time
of measurement by adjusting the resistances of the other
arms. The bridge circuit found in most strain indicators,
on the other hand, is unbalanced by the varying gage
resistance(s) at the time of making the measurement, and
is therefore commonly referred to as the “unbalanced”
Wheatstone bridge.
The output voltage obtained from the “unbalanced”
Wheatstone bridge is a function of the amount of unbalance,
and is therefore directly related to the strain applied to the
strain gage. However, under certain conditions frequently
encountered in actual practice, the bridge output voltage
is, as noted earlier, a nonlinear function of the resistance
change in the bridge arms. When this occurs, the strain
readings will be somewhat in error.

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