Consider a current carrying wire (current $I$ ) in the shape of a circle.

Two batteries of emf $\varepsilon_1$ and $\varepsilon_2\left(\varepsilon_2>\varepsilon_1\right)$ and internal resistances $r_1$ and $r_2$ respectively are connected in parallel as shown in figure.

A resistance $R$ is to be measured using a meter bridge, student chooses the standard resistance $S$ to be $100 \Omega$. He finds the null point at $I_1=2.9 \mathrm{~cm}$. He is told to attempt to improve the accuracy. Which of the following is a useful way?

Two cells of emfs approximately 5 V and 10 V are to be accurately compared using a potentiometer of length 400 cm.

A metal rod of length 10 cm and a rectangular cross-section of $1 \mathrm{~cm} \times \frac{1}{2} \mathrm{~cm}$ is connected to a battery across opposite faces. The resistance will be

Which of the following characteristics of electrons determines the current in a conductor?

Kirchhoff's junction rule is a reflection of

Consider a simple circuit shown in figure stands for a variable resistance $R^{\prime} \cdot R^{\prime}$ can vary from $R_0$ to infinity. $r$ is internal resistance of the battery $(r<< R< R$,$) .$

Temperature dependence of resistivity $\rho(T)$ of semiconductors, insulators and metals is significantly based on the following factors

The measurement of an unknown resistance $R$ is to be carried out using Wheatstones bridge as given in the figure below. Two students perform an experiment in two ways. The first students takes $R_2=10 \Omega$ and $R_1=5 \Omega$. The other student takes $R_2=1000 \Omega$ and $R_1=500 \Omega$. In the standard arm, both take $R_3=5 \Omega$. Both find $R=\frac{R_2}{R_1}, R_3=10 \Omega$ within errors.

In a meter bridge, the point $D$ is a neutral point (figure).

Is the motion of a charge across junction momentum conserving? Why or why not?

The relaxation time $\tau$ is nearly independent of applied $E$ field whereas it changes significantly with temperature $T$. First fact is (in part) responsible for Ohm's law whereas the second fact leads to variation of $p$ with temperature. Elaborate why?

What are the advantages of the null-point method in a Wheatstone bridge? What additional measurements would be required to calculate $R_{\text {unknown }}$ by any other method?

What is the advantage of using thick metallic strips to join wires in a potentiometer?

For wiring in the home, one uses Cu wires or Al wires. What considerations are involved in this?

Why are alloys used for making standard resistance coils?

Power $P$ is to be delivered to a device via transmission cables having resistance $R_c$. If $V$ is the voltage across $R$ and $I$ the current through it, find the power wasted and how can it be reduced.

$A B$ is a potentiometer wire (figure). If the value of $R$ is increased, in which direction will the balance point J shift?

While doing an experiment with potentiometer (figure) it was found that the deflection is one sided and (i) the deflection decreased while moving from one and $A$ of the wire, to the end $R$; (ii) the deflection increased, while the jockey was moved towards the end $D$.

(i) Which terminal positive or negative of the cell $E_1$ is connected at $X$ in case (i) and how is $E_1$, related to $E$ ?

(ii) Which terminal of the cell $E_1$ is connected at $X$ in case (1 in 1 )?

A cell of emf $E$ and internal resistance $r$ is connected across an external resistance $R$. Plot a graph showing the variation of potential differential across $R$, versus $R$.

First a set of $n$ equal resistors of $R$ each are connected in series to a battery of emf $E$ and internal resistance $R, A$ current $I$ is observed to flow. Then, the $n$ resistors are connected in parallel to the same battery. It is observed that the current is increased 10 times. What is ' $n$ ' ?

Let there be $n$ resistors $R_1 \ldots \ldots . R_n$ with $R_{\max }=\max \left(R_1 \ldots \ldots \ldots R_n\right)$ and $R_{\min }=\min \left\{R_{1 . . .} \quad R_n\right\}$. Show that when they are connected in parallel, the resultant resistance $R_p=R_{\min }$ and when they are connected in series, the resultant resistance $R_s>R_{\max }$. Interpret the result physically.

The circuit in figure shows two cells connected in opposition to each other. Cell $E_1$ is of emf 6 V and internal resistance $2 \Omega$ the cell $E_2$ is of emf 4 V and internal resistance $8 \Omega$. Find the potential difference between the points $A$ and $B$.

Two cells of same emf $E$ but internal resistance $r_1$ and $r_2$ are connected in series to an external resistor $R$ (figure). What should be the value of $R$ so that the potential difference across the terminals of the first cell becomes zero?

Two conductors are made of the same material and have the same length. Conductor $A$ is a solid wire of diameter 1 mm . Conductor $B$ is a hollow tube of outer diameter 2 mm and inner diameter 1 mm . Find the ratio of resistance $R_A$ to $R_B$.

Suppose there is a circuit consisting of only resistances and batteries. Suppose one is to double (or increase it to $n$-times) all voltages and all resistances. Show that currents are unaltered. Do this for circuit of Examples 3,7 in the NCERT Text Book for Class XII.

Two cells of voltage 10 V and 2 V and $10 \Omega$ internal resistances $10 \Omega$ and $5 \Omega$ respectively, are connected in parallel with the positive end of 10 V battery connected to negative pole of 2 V battery (figure). Find the effective voltage and effective resistance of the combination.

A room has $A C$ run for 5 a day at a voltage of 220 V . The wiring of the room consists of Cu of 1 mm radius and a length of 10 m . Power consumption per day is 10 commercial units. What fraction of it goes in the joule heating in wires? What would happen if the wiring is made of aluminium of the same dimensions?

$$\left[\rho_{\mathrm{Cu}}=11.7 \times 10^{-8} \Omega \mathrm{~m}, \rho_{\mathrm{Al}}=2.7 \times 10^{-8} \Omega \mathrm{~m}\right]$$

In an experiment with a potentiometer, $V_B=10 \mathrm{~V} . R$ is adjusted to be $50 \Omega$ (figure). A student wanting to measure voltage $E_1$ of a battery (approx. 8V) finds no null point possible. He then diminishes R to $10 \Omega$ and is able to locate the null point on the last (4th) segment of the potentiometer. Find the resistance of the potentiometer wire and potential drop per unit length across the wire in the second case.

(a) Consider circuit in figure. How much energy is absorbed by electrons from the initial state of no current (Ignore thermal motion) to the state of drift velocity ?

(b) Electrons give up energy at the rate of $R I^2$ per second to the thermal energy. What time scale would number associate with energy in problem (a)? $n=$ number of electron/volume $=10^{29} / \mathrm{m}^3$. Length of circuit $=10 \mathrm{~cm}$, cross-section $=A=(1 \mathrm{~mm})^2$.