MCQ I 3.1 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 (a) source of emf. (b) electric field produced by charges accumulated on the surface of wire. (c) the charges just behind a given segment of wire which push them just the right way by repulsion. 13.2 Two batteries of emf ε and ε (ε> ε) and internal 122 1resistances r and r respectively are connected in parallel 12AB as shown in Fig 3.1. (a) The equivalent emf ε eq of the two cells is between ε1 and ε, i.e. ε< ε < ε.21eq 2Fig 3.1 (b) The equivalent emf ε eq is smaller than ε1 . (c) The ε eq is given by ε eq = ε1 + ε2 always. (d) ε eq is independent of internal resistances r1 and r2. 3.3 A resistance R is to be measured using a meter bridge. Student chooses the standard resistance S to be 100Ω. 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? (a) He should measure l1 more accurately. (b) He should change S to 1000Ω and repeat the experiment. (c) He should change S to 3Ω and repeat the experiment. (d) He should give up hope of a more accurate measurement with a meter bridge. 3.4 Two cells of emf’s approximately 5V and 10V are to be accurately compared using a potentiometer of length 400cm. (a) The battery that runs the potentiometer should have voltage of 8V. (b) The battery of potentiometer can have a voltage of 15V and R adjusted so that the potential drop across the wire slightly exceeds 10V. (c) The first portion of 50 cm of wire itself should have a potential drop of 10V. (d) Potentiometer is usually used for comparing resistances and not voltages. 3.5 A metal rod of length 10 cm and a rectangular cross-section of 1 1cm × cm is connected to a battery across opposite faces. The 2resistance will be 1 (a) maximum when the battery is connected across 1 cm × cm2faces. (b) maximum when the battery is connected across 10 cm × 1 cm faces. 1 (c) maximum when the battery is connected across 10 cm × 2cm faces. (d) same irrespective of the three faces. 3.6 Which of the following characteristics of electrons determines the current in a conductor? (a) Drift velocity alone. (b) Thermal velocity alone. (c) Both drift velocity and thermal velocity. (d) Neither drift nor thermal velocity. 17 MCQ II 3.7 Kirchhoff ’s junction rule is a reflection of (a) conservation of current density vector. (b) conservation of charge. (c) the fact that the momentum with which a charged particle approaches a junction is unchanged (as a vector) as the charged particle leaves the junction. (d) the fact that there is no accumulation of charges at a junction. 3.8 Consider a simple circuit shown in Fig 3.2. stands for a I A V R r Fig 3.2 B variable resistance R ′. R ′ can vary from R0 to infinity. r is internal resistance of the battery (r< R max. Interpret the result physically. The circuit in Fig 3.6 shows two cells connected in opposition to A B each other. Cell E1 is of emf 6V and internal resistance 2Ω; the E1 E2 cell E2 is of emf 4V and internal resistance 8Ω. Find the potential difference between the points A and B. Fig 3.6 Two cells of same emf E butE E 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. 20 3.26 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 RA to RB. 3.27 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 Example 3.7 in the NCERT Text Book for Class XII. LA 3.28 Two cells of voltage 10V and 2V and internal resistances 10Ω and 5Ω respectively, 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. 3.29 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 aluminium of the same dimensions? = 1.7 × , ρ= 2.7 × 10–8 Ωm][ρ cu 10Ω–8 m Al 3.30 In an experiment with a potentiometer, VB = 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 (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. 3.31 (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 R I 2V I2 10 I110V Fig 3.8 E11E2 3 A2 B N1R ( ) C K1 Fig 3.9 R= 6 I I Fig 3.10 21