Discover the Formula for Calculating Potential Difference with a Potentiometer

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The discussion focuses on calculating the potential difference using a potentiometer, specifically the relationship V=(x/l)E, where V is the unknown potential difference and E is the electromotive force (emf). The setup includes a uniform wire resistor with a sliding contact that divides the wire into two segments, R_1 and R_2, proportional to their lengths x and l-x. The current through the circuit is determined by the total resistance, and the potential difference across R_1 can be expressed in terms of the current and its resistance. Understanding these relationships allows for the determination of the unknown potential difference when the galvanometer reads zero.
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I have a homework question about a potentiometer. There is a resistor between a and b that is a uniform wire of length l, with a sliding contact c at a distance x from b. An unknown potential difference V is measured by sliding the contact until the galvonometer G reads zero. I need to show that under this condition the unknown potential difference is given by V=(x/l)E. Any ideas?
 
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What is meant by E?
 
npgreat said:
What is meant by E?

E is the emf.
 
The sliding contact divides the resistor in two other resistors R=R_1+R_2 where R_1 and R_2 are proportional with corresponding lengths (x and l-x). The current is given by
I=\frac{E}{R}
and the potential difference between the ends of R_1
V=I\cdot R_1
and so on...
 
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Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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