Asok Kumar Das and Chittaranjan Dasgupta Solutions for Chapter: Current Electricity, Exercise 1: EXERCISE 5

The given graph shows the variation of resistance of mercury in the temperature range $\mathrm{O}< \mathrm{T}< 4\mathrm{K}.$ Name the phenomenon shown by the graph of figure.

A secondary cell of emf $\mathrm{E}$ is being charged by an external supply. Its terminal voltage during charging is $\mathrm{V}$. Compare $\mathrm{E}$ and $\mathrm{V}$.

The figure, Fig. $5.163$ Shows a potentiometer with a cell of $2.0 \mathrm{V}$ And internal resistance $0.40\Omega$ Maintaining a potential.

Drop across a resistor wire $\mathrm{AB}$ A standard cell which maintains a constant emf of $1.02 \mathrm{V}$ (for very moderate current currents up to a few $\mu \mathrm{A}$ ) gives a balance point at $67.3 \mathrm{cm}$ Length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of $600\mathrm{k}\Omega$ Is put in series with it, which is shorted close to balance point. The standard cell is then replaced by a cell of unknown emf $\in$ And the balance point found similarly turns out to be at $82.3 \mathrm{cm}$ Length of the wire.

(a) What is the value of $\in$?

The figure, Fig. $5.163$ Shows a potentiometer with a cell of $2.0 \mathrm{V}$ And internal resistance $0.40\Omega$ Maintaining a potential

Drop across a resistor wire $\mathrm{AB}$ A standard cell which maintains a constant emf of $1.02 \mathrm{V}$ (for very moderate current currents up to a few $\mu \mathrm{A}$ ) gives a balance point at $67.3 \mathrm{cm}$ Length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of $600\mathrm{k}\Omega$ Is put in series with it, which is shorted close to balance point. The standard cell is then replaced by a cell of unknown emf $\in$ And the balance point found similarly turns out to be at $82.3 \mathrm{cm}$ Length of the wire.

(b) What purpose does the high resistance of $6000\mathrm{k}\Omega$.

The figure, Fig. $5.163$ Shows a potentiometer with a cell of $2.0 \mathrm{V}$ And internal resistance $0.40\Omega$ Maintaining a potential

Drop across a resistor wire $\mathrm{AB}$ A standard cell which maintains a constant emf of $1.02 \mathrm{V}$ (for very moderate current currents up to a few $\mu \mathrm{A}$ ) gives a balance point at $67.3 \mathrm{cm}$ Length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of $600\mathrm{k}\Omega$ Is put in series with it, which is shorted close to balance point. The standard cell is then replaced by a cell of unknown emf $\in$ And the balance point found similarly turns out to be at $82.3 \mathrm{cm}$ Length of the wire.

(c) Is the balance point effect by this high resistance?

The figure, Fig. $5.163$ Shows a potentiometer with a cell of $2.0 \mathrm{V}$ And internal resistance $0.40\Omega$ Maintaining a potential

Drop across a resistor wire $\mathrm{AB}$ A standard cell which maintains a constant emf of $1.02 \mathrm{V}$ (for very moderate current currents up to a few $\mu \mathrm{A}$ ) gives a balance point at $67.3 \mathrm{cm}$ Length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of $600\mathrm{k}\Omega$ Is put in series with it, which is shorted close to balance point. The standard cell is then replaced by a cell of unknown emf $\in$ And the balance point found similarly turns out to be at $82.3 \mathrm{cm}$ Length of the wire.

(d) Is the balance point affected by the internal resistance of the driver cell?

The figure, Fig. $5.163$ Shows a potentiometer with a cell of $2.0 \mathrm{V}$ And internal resistance $0.40\Omega$ Maintaining a potential

Drop across a resistor wire $\mathrm{AB}$ A standard cell which maintains a constant emf of $1.02 \mathrm{V}$ (for very moderate current currents up to a few $\mu \mathrm{A}$ ) gives a balance point at $67.3 \mathrm{cm}$ Length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of $600\mathrm{k}\Omega$ Is put in series with it, which is shorted close to balance point. The standard cell is then replaced by a cell of unknown emf $\in$ And the balance point found similarly turns out to be at $82.3 \mathrm{cm}$ Length of the wire.

(e) Would the method work in the above solution if the driver cell of potentiometer had an emf of $1.0 \mathrm{V}$ Instead of $2.0 \mathrm{V}$?

The figure, Figure shows a potentiometer with a cell of $2.0 \mathrm{V}$ and internal resistance $0.40 \Omega$ maintaining a potential drop across a resistor wire $\mathrm{AB}$ A standard cell which maintains a constant emf of $1.02 \mathrm{V}$ (for very moderate current currents upto a few $\mu \mathrm{A}$ ) gives a balance point at $67.3 \mathrm{cm}$ length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of $600 \mathrm{k\Omega }$ is put in series with it, which is shorted close to balance point. The standard cell is then replaced by a cell of unknown emf $\in$ and the balance point found similarly turns out to be at $82.3 \mathrm{cm}$ length of the wire. Would the circuit work well for determining an extremely small emf, say of the order of a few $\mathrm{mV}$ (such as the typical emf of the thermocouple)? If now, how will you modify the circuit.