In experiment of the potentiometer wire AB of length 100 cm has a resistance of 10 Ω. It is con

step 1 In this question we have a length hundred centimeters and resistance 10 oms so resistance per un

In experiment of the potentiometer wire AB of length 100 cm...

In experiment of the potentiometer wire $\mathrm{AB}$ of length $100 \mathrm{~cm}$ has a resistance of $10 \Omega$. It is connected in series with a resistance $\mathrm{R}$ and a cell of emf 2 volts and of negligible internal resistance. A source emf $10 \mathrm{mV}$ is balanced against a length of $40 \mathrm{~cm}$ of the potentiometer wire. What is the value of the external resistance? (A) $900 \Omega$ (B) $820 \Omega$ (C) $790 \Omega$ (D) $670 \Omega$

In experiment of the potentiometer wire $\mathrm{AB}$ of length $100 \mathrm{~cm}$ has a resistance of $10 \Omega$. It is connected in series with a resistance $\mathrm{R}$ and a cell of emf 2 volts and of negligible internal resistance. A source emf $10 \mathrm{mV}$ is balanced against a length of $40 \mathrm{~cm}$ of the potentiometer wire. What is the value of the external resistance?
(A) $900 \Omega$
(B) $820 \Omega$
(C) $790 \Omega$
(D) $670 \Omega$

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Key Concepts

Potentiometer Principle

The potentiometer is an instrument that uses a uniform resistance wire to measure the potential difference in a circuit. By moving a contact along the wire until a null (balanced) condition is achieved against an unknown emf, the instrument allows for precise determination of voltage without drawing current from the source being measured.

Potential Gradient

The potential gradient is the voltage drop per unit length along a uniform resistor or potentiometer wire. It is a crucial concept because it establishes a linear relationship between length and voltage, enabling the determination of voltage differences by measuring distances along the wire.

Voltage Division in Series Circuits

In a series circuit, the total emf provided by the battery is divided among the circuit components in proportion to their resistances. This division of voltage is key to understanding how the voltage across the potentiometer wire is determined when it is connected in series with an external resistance.

Ohm's Law

Ohm's Law relates the voltage, current, and resistance in an electrical circuit through the formula V = IR. This fundamental law is used to analyze the behavior of electrical circuits, particularly in determining the current through and voltage across various components in series circuits.

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