 # Wheatstone bridge, Meter bridge and Potentiometer

• Condition for balanced Wheatstone bridge \tt \frac{P}{Q} = \frac{R}{S}
• In balanced meter bridge \tt \frac{resistance \ in \ left \ gap}{resistance \ in \ Right \ gap} = \frac{l}{100 - l}
• A High resistance is connected in series to galvanometer to protect it from high currents.
• Potentiometer is an ideal voltmeter.
• Potentiometer is used to measure unknown emf of cell.
• Potentiometer is used to measure internal resistance of cell.
• Principle of potentiometer is potential difference across the balancing length of potentiometer wire is equal to emf of the cell in the secondary circuit.
• Potential drop per unit length of potentiometer wire is called potential gradient.
• Potential gradient = \tt \frac{iR}{L} = \frac{Ep}{R + Rs + r_{o}} . \frac{R}{L}
• l1 and l2 are the balancing lengths of two cells of emf’s E1 and E2 then \tt \frac{E_{1}}{E_{2}} = \frac{l_{1}}{l_{2}}
• If "l1" is the balancing length, a known resistance ‘R’ is connected across the cell the balancing length becomes "l2" then internal resistance \tt r = \left(\frac{l_{1}-l_{2}}{l_{2}}\right) R

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1. Principle of Wheatstone Bridge
\frac{P}{Q} = \frac{R}{S}

2. Meter Bridge
\frac{R}{S} = \frac{l_{1}}{(100 - l_{1})}

3. Potentiometer will be
K = \frac{V}{L} = \frac{IR}{L}
= \frac{E_{0}R}{(R_{0} + R)L}

4. Determination of emf of a Cell using potentiometer
E = Kl
\frac{E_{1}}{E_{2}} = \frac{l_{1}}{l_{2}}

5. Determination of internal Resistance of a Cell using potentiometer
r = \frac{E - V}{V} R = \frac{l_{1} - l_{2}}{l_{2}} R