Physics

The circuit in figure shows two cells connected in opposition to each other. Cell E₁is of emf 6 V and internal resistance 2 Ω; the cell E₂ is of emf 4 V and internal resistance 8 Ω. Find the potential difference between the points A and B.

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 / 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 V?

Consider a heat engine as shown in Fig. Q₁ and Q₂ are heat added to heat bath T₁ and heat taken from T₂ in one cycle of engine. W is the mechanical work done on the engine. If W > 0, then possibilities are:

(a) Q₁ > Q₂ > 0

(b) Q₂ > Q₁ > 0

(c) Q₂ < Q₁ < 0

(d) Q₁ < 0, Q₂ > 0

Consider a cycle followed by an engine 1 to 2 is isothermal 2 to 3 is adiabatic 3 to 1 is adiabatic Such a process does not exist because

(a) Heat is completely converted to mechanical energy in such a process, which is not possible.

(b) Mechanical energy is completely converted to heat in this process, which is not possible.

(c) Curves representing two adiabatic processes don't intersect.

(d) Curves representing an adiabatic process and an isothermal process don't intersect.

Figure 12.5 shows the P-V diagram of an ideal gas undergoing a change of state from A to B. Four different parts I, II, III and IV as shown in the figure may lead to the same change of state.

(a) Change in internal energy is same in IV and III cases, but not in I and II

(b) Change in internal energy is same in all the four cases

(c) Work done is maximum in case I

(d) Work done is minimum in case II

An ideal gas undergoes isothermal process from some initial state i to final state f. Choose the correct alternatives.

(a) dU = 0

(b) dQ= 0

(c) dQ = dU

(d) dQ = dW

Which of the processes described below are irreversible?

(a) The increase in temperature of an iron rod by hammering it

(b) A gas in a small container at a temperature T₁ is brought in contact with a big reservoir at a higher temperature T₂ which increases the temperature of the gas

(c) A quasi-static isothermal expansion of an ideal gas in cylinder fitted with a frictionless piston

(d) An ideal gas is enclosed in a piston cylinder arrangement with adiabatic walls. A weight W is added to the piston, resulting in compression of gas

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

Three copper blocks of masses M₁, M₂ and M₃ kg respectively are brought into thermal contact till they reach equilibrium. Before contact, they were at T₁, T₂, T₃ (T₁ > T₂ > T₃ ). Assuming there is no heat loss to the surroundings, the equilibrium temperature T is (s is specific heat of copper)

(a) T= $\frac{{\mathit{T}}_1+{\mathit{T}}_2+{\mathit{T}}_3}{3}$

(b) T= $\frac{{\mathit{M}}_1{\mathit{T}}_1+{\mathit{M}}_2{\mathit{T}}_2+{\mathit{M}}_3{\mathit{T}}_3}{{\mathit{M}}_1+{\mathit{M}}_2+{\mathit{M}}_3}$  

(c)  T= $\frac{{\mathit{M}}_1{\mathit{T}}_1+{\mathit{M}}_2{\mathit{T}}_2+{\mathit{M}}_3{\mathit{T}}_3}{3({\mathit{M}}_1+{\mathit{M}}_2+{\mathit{M}}_3)}$

(d) T= $\frac{{\mathit{M}}_1{\mathit{T}}_1\mathit{s}+{\mathit{M}}_2{\mathit{T}}_2\mathit{s}+{\mathit{M}}_3{\mathit{T}}_3\mathit{s}}{{\mathit{M}}_1+{\mathit{M}}_2+{\mathit{M}}_3}$   

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 end 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 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)?