Determination of L by Anderson's Bridge(R.H 01.03.22).pptx
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The document describes a method to determine the self-inductance of a coil using Anderson's Bridge. The method involves first using a DC Wheatstone bridge circuit to measure the coil's resistance, and then using an AC Wheatstone bridge circuit with a variable capacitor and resistor to balance the bridge and calculate the self-inductance from the circuit values. The theory section explains how Kirchhoff's laws are applied to the AC bridge circuit to derive the formula used to determine the self-inductance.
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- Quality factor Q relates bandwidth to center frequency. As Q increases, bandwidth decreases. Q is proportional to center frequency and inversely proportional to bandwidth.
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Resonance is an important phenomenon in electrical applications such as telecommunications. A resonant circuit occurs when the voltage and current are in phase, resulting in zero net reactance and behaving like a pure resistor. There are two types of resonance: series and parallel. In series resonance, the potential differences across the inductor and capacitor cancel out, resulting in maximum voltage magnification. The bandwidth of a resonant circuit is defined as the range of frequencies where the power delivered is greater than or equal to half the power at resonance.
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- 2. DC Balance • The experiment is performed in two stages. DC Balance • The circuit connections are shown in Figure. • The given coil of self inductance L and resistance S is connected in arm DC. • The values of P and Q are fixed to ratio 1:1. • The resistance R is adjusted for balance. • This gives the approximate value of resistance S of the coil. • The experiment is repeated by making the P:Q ratio to be 10:1 and 100:1. • The accurate value of D.C resistance of the coil is found by the wheatstone’s bridge relation, • 𝑃 𝑄 = 𝑅 𝑆 or S = R 𝑄 𝑃
- 4. AC BALANCE • An ac source is connected between A and C (Figure.B) • A variable non-inductive resistance r is connected in series with a capacitance C and this combination is connected between in parallel with the arm AB. • A headphone H is connected between E and D. • The resistance r is adjusted until minimum sound is heard in the headphone. • The value f L is calculated using the formula • L = C[RQ + r (R + S)]
- 5. THEORY • Let the instantaneous currents in the different arms be as shown in the different arms be as shown in figure B. • As the time of balance (i.e. no current through headphone). • Potential at E = potential at D. • Applying Kirchoff’s II law, we have • For mesh ABEA,
- 7. Here 1/jωC and jωL are the impedances offered by capacitor C and inductance L respectively. Ω is the angular frequency of applied ac. Substituting Eqs. (1) and (2) in Eq.(3). We get
- 9. L = C[Sr + RQ + Rr] L = C [RQ + r (R+S)]
- 10. THANK YOU