A 10 m long wire of uniform cross-section and 20 $\Omega$ resistance is used in a potentiometer. The wire is connected in series with a battery of 5V along with an external resistance of 480 $\Omega$. If an unknown emf E is balanced at 6.0 m length of the wire, calculate:
- The potential gradient of the potentiometer wire.
- The value of unknown emf E.
CBSE DELHI - SET 1 2006
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Current I $= \frac{5}{480+20}= 0.01\text{A}$$\therefore $ p.d.across the wire (dV) = IR = 0.1X20=0.2V
Potental gradient $\big(\triangle\text{V}\big)\frac{\text{dV}}{\text{dx}}= \frac{0.2}{10}\frac{\text{V}}{m}=0.02\text{Vm}^{-1}$
E.M.F. Of the cell $\varepsilon= \bigtriangleup\text{V}\times$ balance lentgh
=0.02X6 = 0.12 V
Potental gradient $\big(\triangle\text{V}\big)\frac{\text{dV}}{\text{dx}}= \frac{0.2}{10}\frac{\text{V}}{m}=0.02\text{Vm}^{-1}$
E.M.F. Of the cell $\varepsilon= \bigtriangleup\text{V}\times$ balance lentgh
=0.02X6 = 0.12 V
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