Solution of Chapter 3. Current Electricity (Physics - Exemplar Book)

Consider a current carrying wire (current I) in the shape of a circle. Note that as the current progresses along the wire, the direction of j (current density) changes in an exact manner, while the current I remain unaffected. The agent that is essentially responsible for is

Two batteries of emf ε₁ and ε₂ (ε₂ > ε₁) and internal resistances r₁ and r₂ respectively are connected in parallel as shown in Fig 3.1.

A resistance R is to be measured using a meter bridge. Student chooses the standard resistance S to be 100. He finds the null point at l1 = 2.9 cm. He is told to attempt to improve the accuracy. Which of the following is a useful way?

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

A metal rod of length 10 cm and a rectangular cross-section of 1cm × 1/2 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 Fig 3.2. variable resistance R’. R’ can vary from R₀ to infinity. r is internal resistance of the battery (r<<R<<R₀).

Temperature dependence of resistivity ρ(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 Wheat stones bridge (see Fig. 3.25 of NCERT Book). Two students perform an experiment in two ways. The first students take R₂ = 10Ω and R₁ = 5 Ω. The other student takes R₂ = 1000 Ω and R₁ = 500 Ω. In the standard arm, both take R₃ = 5 Ω. Both find within errors.

In a meter bridge the point D is a neutral point (Fig 3.3).

A. The meter bridge can have no other neutral point for this set of resistances.

B. When the jockey contacts a point on meter wire left of D, current flows to B from the wire.

C. When the jockey contacts a point on the meter wire to the right of D, current flows from B to the wire through galvanometer.

D. When R is increased, the neutral point shifts to left.

Is the momentum conserved when charge crosses a junction in an electric circuit? Why or why not?

The relaxation time τ 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 ρ 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_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.

AB is a potentiometer wire (Fig 3.4). If the value of R is increased, in which direction will the balance point J shift?

While doing an experiment with potentiometer (Fig 3.5) it was found that the deflection is one sided and (i) the deflection decreased while moving from one end A of the wire to the end B; (ii) the deflection increased. While the jockey was moved towards the end B.

(i) Which terminal +or –ve of the cell E₁, is connected at X in case (i) and how is E₁ related to E?

(ii) Which terminal of the cell E₁ is connected at X in case (ii)?

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 R₁ ............R_n with R_max = max (R₁......... R_n) and R_min = min {R₁ ..... R_n}. 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 Fig 3.6 shows two cells connected in opposition to each other. Cell E₁ is of emf 6V and internal resistance 2 Ω; the cell E₂ is of emf 4V and internal resistance 8Ω. Find the potential difference between the points A and B.

Two cells of same emf E but internal resistance r₁ and r₂ are connected in series to an external resistor R (Fig 3.7). 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 1mm. Conductor B is a hollow tube of outer diameter 2mm and inner diameter 1mm. Find the ratio of resistance R_A to R_B.

Suppose there is a circuit consisting of only resistances and batteries and we have to double (or increase it to n-times) all voltages and all resistances. Show that currents are unaltered. Do this for circuit of Example 3.7 in the NCERT Text Book for Class XII.

Two cells of voltage 10V and 2V and internal resistances 10Ω and 5Ωrespectively, are connected in parallel with the positive end of 10V battery connected to negative pole of 2V battery (Fig 3.8). Find the effective voltage and effective resistance of the combination.

A room has AC run for 5 hours a day at a voltage of 220V. 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 aluminum of the same dimensions?

[ρ_cu = 1.7 × –8¹⁰_Ωm, ρ_Al = 2.7 × 10^–8 Ωm]

In an experiment with a potentiometer, V_B = 10V. R is adjusted to be 50Ω (Fig. 3.9). A student wanting to measure voltage E₁ of a battery (approx. 8V) finds no null point possible. He then diminishes R to 10Ω and is able to locate the null point on the last (4^th) 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 Fig 3.10. 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 RI₂ per second to the thermal energy. What time scale would one associate with energy in problem (a)? n = no of electron/volume = 10²⁹/m³, length of circuit = 10 cm, cross-section = A = (1mm)²