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<p><b>New page</b></p><div>{{Short description|Circuit in electronics}}<br />
[[File:Andersons-bridge-circuit.jpg|thumb|right|Anderson's bridge]]<br />
In [[Engineering:Electronics|electronics]], '''Anderson's bridge''' is a [[Engineering:Bridge circuit|bridge circuit]] used to measure the self-inductance of the coil. It enables measurement of inductance by utilizing other circuit components like resistors and capacitors.<ref>[https://nvlpubs.nist.gov/nistpubs/bulletin/01/nbsbulletinv1n3p291_A2b.pdf Measurement of inductance by Anderson's Method] By Edward B. Rosa and Fredeeick W. Grover, Bulletin of the Bureau of Standards, Vol 1, No 3</ref><br />
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Anderson's bridge was invented by Alexander Anderson in 1891.<ref>[https://circuitglobe.com/andersons-bridge.html Anderson’s Bridge] Circuit Globe</ref> He modified [[Physics:Maxwell bridge|Maxwell's inductance capacitance bridge]] so that it gives very accurate measurement of self-inductance.<ref>S. Butterworth (December 1921) ''[https://xueshu.baidu.com/usercenter/paper/show?paperid=2379fe40e571483c7fa1d91cd4991c96 On The Use of Anderson's Bridge for the Measurement of the Variations of the Capacity and Effective Resistance of a Condenser with Frequency]'', ''Proceedings of the Physical Society of London'', Dec 1921, vol. 34, pages 1–7</ref><br />
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== Balance conditions ==<br />
The balance conditions for Anderson's bridge or, equivalently the values of the self-inductance and resistance of the given coil can be found using basic circuit analysis techniques such as KCL, KVL and using phasors.<br />
Consider the circuit diagram of Anderson's bridge in the given figure. Let '''L<sub>1</sub>''' be the self-[[Physics:Inductance|inductance]] and '''R<sub>1</sub>''' be the [[Physics:Electrical resistance|electrical resistance]] of the coil under consideration. Since the voltmeter is ideally assumed to have nearly infinite impedance, the currents in branches '''ab''' and '''bc''' and those in the branches '''de''' and '''ec''' are taken to be equal. Applying [[Kirchhoff's circuit laws|Kirchhoff's current law]] at node d, it can be shown that-<br />
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:<math>\begin{align}<br />
I_4 + I_c &= I_2<br />
\end{align}</math><br />
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Since the analysis is being made under the balanced condition of the bridge, it can be said that the voltage drop across the voltmeter is essentially zero. On applying [[Kirchhoff's circuit laws|Kirchhoff's voltage law]] to the appropriate loops(in the anti-clockwise direction), the following relations hold-<br />
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:<math>\begin{align}<br />
I_1(R_1 + r_1 + j \omega L_1) - I_2 R_2 - I_c r = 0 \\<br />
I_1 R_3 - \frac{I_c}{j \omega C} = 0 \\<br />
I_c r + \frac{I_c}{j \omega C} - I_4 R_4 = 0<br />
\end{align}</math><br />
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On solving these sets of equations, one can finally obtain the self-inductance and resistance of the coil as-<br />
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:<math>\begin{align}<br />
L_1 &= (\frac{R_3}{R_4})(R_2 R_4 + r(R_2 + R_4))C \\<br />
R_1 &= \frac{R_2 R_3}{R_4} - r_1<br />
\end{align}</math><br />
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== Advantages ==<br />
The Anderson's bridge can also be used the other way round- that is, it can be used to measure the capacitance of an unknown [[Engineering:Capacitor|capacitor]] using an inductor coil whose self-[[Physics:Inductance|inductance]] and [[Physics:Electrical resistance|electrical resistance]] have been pre-determined to a high degree of precision. An interesting point to note is the fact that the measured self-inductance of the coil does not change even on taking [[Physics:Dielectric loss|dielectric loss]] within the [[Engineering:Capacitor|capacitor]] into account. Another advantage of using this modified bridge is that unlike the variable capacitor used in [[Physics:Maxwell bridge|Maxwell bridge]], it makes use of a fixed capacitor which is relatively quite cheaper.<ref>{{cite web | url=https://www.electricaldeck.com/2021/06/andersons-bridge-circuit-construction-equation-phasor-diagram-advantages.html | title=Anderson's Bridge - Circuit Construction, Equation, Phasor Diagram & Advantages }}</ref><br />
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== Disadvantages ==<br />
One of the obvious difficulties associated with Anderson's bridge are the relatively complex balance equation calculations compared to the [[Physics:Maxwell bridge|Maxwell bridge]]. The circuit connections and computations are similarly more cumbersome in comparison to the [[Physics:Maxwell bridge|Maxwell bridge]].<ref>{{cite web | url=https://www.electricaldeck.com/2021/06/andersons-bridge-circuit-construction-equation-phasor-diagram-advantages.html | title=Anderson's Bridge - Circuit Construction, Equation, Phasor Diagram & Advantages }}</ref><br />
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==References==<br />
{{Reflist|30em}}<br />
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{{Bridge circuits}}<br />
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[[Category:Measuring instruments]]<br />
[[Category:Bridge circuits]]<br />
[[Category:Analog circuits]]<br />
[[Category:Impedance measurements]]<br />
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{{Sourceattribution|Anderson's bridge}}</div>Steve2012