physics for you February 11 Page 68

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Ernest Garrison
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1 urrent Electricity Passage 1 4. f the resistance of a 1 m length of a given wire t is observed that good conductors of heat are also is W, and it carried a current 1, the good conductors of electricity. electric field is n fact, the ratio of thermal conductivity to the heat (a) V conductivity is almost a constant. t very low (b) V m 1 temperatures, this relation is not accurate. (c) greater than V m 1 s the kinetic theory of gases was already developed, (d) less than V m 1 this was extended by Lorentz to electrical conduction 5. The drift velocity is very small; but it is found that also. as soon as one switches on the lights at home, the However the calculated value of vrms according to the bulb immediately glows. This is because kinetic theory of gas was much higher when compared (a) the electrons travel very fast. to that of an electron. However broad comparison of (b) the electric field travels very fast. methods still holds. (c) this depends on the circuit. 1. The formula for the value of vrms of gas molecules. 3kT =. 6. The resistivity of a metal normally m (a) increases with temperature y the same analogy, the value of the drift velocity (b) decreases with temperature of the electron at the same temperature is (c) does not change (a) equal to that of the gas molecule (b) more than that of the gas molecule, as the mass of the electron is much smaller than that of the 7. The resistivity for mercury, hafnium and certain other alloys falls below zero for very low gas molecule temperatures. They are called (c) because electrons flow the same law (a) semiconductors (b) super conductors. s the electron is making constant collision at the (c) any normal conductor behaves like this average interval of time t, the acceleration is only for the time t when due to collision it loses its Passage velocity and again starts from zero. The value of drift velocity is Every electrical circuit, d.c. or a.c., has three important (a) proportional to the potential difference. components. capacitor stores energy, an inductor (b) inversely proportional to the potential behaves like inertia and a resistor dissipates energy. difference. resistance is also used in a heater, furnace or press (c) independent of the potential difference. t is a where the heat produced is useful. t is also used as constant. room-heaters for boiling water, etc. (d) it depends on the field. While the behaviour of a capacitor and inductor is 3. V = (Ohm's law) more useful with alternating current, the resistance is Therefore the current density is widely used both in a.c. as well as d.c. appliances. (a) proportional to conductivity of the metal 8. The power consumed in a resistance when a (b) proportional to the resistivity potential difference V is applied is (c) proportional to the field V (b) V (c) (d) (a) V V physics for you february Page 67

2 68 physics for you February 11 Page 68

3 9. The reason why during long transmission, one uses higher voltages is because (a) the power consumed during transmission is more for high voltage. (b) the power consumed is less for high voltage. (c) it depends on the temperature. (d) one cannot say. Passage 3 Kirchhoff's laws :. Law of the junction 1 O 5 3 When currents 1, enter a junction and currents 3, 4, 5 flow out, whatever current enters the junction, flows out of the junction = 0. When current flows from to, the potential difference is negative. When one takes the potential from to, it is positive. (Up the current flow potential difference is positive). For the loop, + e = 0. These two laws are extremely useful to find the parameters such as current, voltage and resistance in complicated loops. 10. Show that when resistances are connected in series, the same current is flowing, through the resistances f 1 > (a) the potential difference across resistance 1 is greater than of. (b) potential difference across is greater as this resistance is smaller. (c) the potential differences are the same across as well as 1. (d) One must know the value of the emf applied The emf of a aniel cell is 1.08 V and the internal resistance is 10 W. The current flowing through two resistances of 100 W each connected in parallel in the circuit is (a) more than (b) less than but more than 1 (c) less than 0.0 (d) more than f the voltmeter is connected across the cell in the Q. No. 1, the potential difference across the cell is (a) more than the emf (b) less than the emf (c) equal to the emf (d) equal to 1.08 V 14. f a wire of negligible resistance is connected across the battery in Q. No. 1, the current in the wire is (a) 1.08 (b) (c) this will short the battery, the current will be too high Passage 4 t is seen that when two resistances are connected in series, the resistance gets added up, and when connected in parallel, the effective resistance is smaller than the smallest. This idea is used in converting a galvanometer into an ammeter or a voltmeter. 15. n ammeter and a voltmeter are connected in a circuit containing a battery and an external One has to measure the current passing through the resistance and as the potential difference. The meters are connected as follows. (a) The ammeter is connected in series with the (b) The voltmeter is connected in series with the (c) The ammeter is connected in parallel with the (d) The voltmeter is connected in parallel across the resistance to measure the potential difference. 16. To measure the current passing through a particular part of the circuit, the ammeter is connected in series. To convert a moving coil galvanometer into an ammeter, resistance is connected so that the full current passing through the ammeter is not dissipated. How is the galvanometer converted to an ammeter? physics for you february Page 69

4 17. How is the voltmeter connected in a circuit to measure the potential difference across the wire? 18. The essential principle of the Wheatstone bridge is in the given circuit, no current 1 will be flowing through the galvanometer. f 1 = 1 W, G = W, and one has also 3 W, 5 W and 6 W, 3 and are replaced by (a) 3 W, 5 W (b) 5 W, 6 W (c) 3 W, 6 W (d) 6 W, 3 W What is the total resistance connected to the battery? 0. ll resistances are equal. The total resistance between and is O (a) (b) 6 3 (c) 8 1. Length of and are the same but is thicker than. (a) The current density in is the same as that in. (b) The field in > the field in. (c) The current in the thicker wire > the current in the thinner wire. (d) The current is the same in and.. hoose the right statement (a) The current passing through the branch > the current through. (b) The current through > the current through. (c) The currents through, and are the same. (d) There is current only through. 3. The equivalent resistance between and is (a) 4. (b) (c) Give the equivalent diagram. SOLUTONS 3 (d) 1. (d) : v rms for the electron = 3kT m e = m s 1 This will be much higher than that of the gas. This should be (b). However this theory is not applicable; therefore (d).. (d) : The drift velocity = qe m τ s initial velocity = 0 after every collision, v = acceleration time 3. (a, c) : V = l V = ρ V = Field E l = J 70 physics for you February 11 Page 70

5 El = ρ l = = J J 1 ρ E J σ E 4. (b) : V = ; V = (1 ) ( W) V = V m 1 L 5. (b) : The velocity of the electric field is the velocity of light. t is the field that causes current to flow and not the electrons that travel from one end to the other. 6. (a) : The resistivity and hence the resistance increases with temperature. This is the principle of the platinum resistance thermometer. 7. (b) : They are superconductors. The theory of superconductivity will be studied by you later as quantum mechanics is applied for this study. 8. (b) : The work done per second is the power consumed. Work done is Vq and per second, it is V q = V t Unlike the situation in charging a capacitor, the moment the potential difference is applied, the maximum current flows in the resistor, unlike a capacitor where work done is 1 qv. The current is also not a constant when charging or discharging a capacitor. 9. (b) : When power is taken through long wires, as 10. P = V = P V. The power loss along the transmission lines is = = P V For a given resistance, as power loss is inversely proportional to V, higher the transmission voltage, lower is the power loss, when transmitting a given power and given transmission wires. 1 3 t, when, is entering from, flows out of. Therefore the current entering, is the same through 1. Similarly by taking points, successively, one finds, the same current is flowing through and (c) : 1 1 pplying the second law of Kirchhoff, in the loop, = 0. t follows 1 1 =. The potential difference along the path as well as are the same. However as 1 is greater, the current is smaller than that through. 1. (c) : 1.08 V 10 r r is the internal The resistance of 100 W and 100 W in parallel = The total resistance in parallel = 50 W The total resistance in the circuit = = 60 W The current in the circuit = = (c, d) : When the cell is not connected to an external resistance, the potential difference across the cell is emf, 1.08 V. 14. (b) : The internal resistance of this battery is rather high (10 W) as given in Q. No. 1. Therefore the current flowing will be V Ω = 15. (a, d) V 16. The current passing through which the circuit should not be disturbed. Therefore the ammeter which is connected in series with the circuit should pass all the current i.e. the ammeter must have low This is achieved by connecting a thick wire of low resistance in parallel (shunting) to the ammeter. 17. The voltmeter is connected in parallel so that the current passing through the voltmeter is negligible. high resistance is connected in series with the galvanometer. high resistance is in series with the galvanometer so that its effective resistance is very high. The dissipation of the current through the voltmeter will be negligible. physics for you february Page 71

6 18. (c) : G,O, 3 4 f galvanometer gives null position, V = V. is common for and. \ V V = V V. Similarly, V V should be equal to V V. is common. V V = = V V = s = = = 4 6 The other combinations for 3 and 4 do not fit the Wheastone's bridge. 19. One can find various problems of this type. The method of solution is the same. Let the total resistance to right of be X. The circuit is now 1 W is connected in parallel with X which gives X = + X X s this is an infinite series, is also equal to X. + X X = + X X X + 1 = Total resistance where 1 W is the resistance of X i. e. + 1 = X, the total resistance + X X X = 0 X = ± + Total resistance, X = W as the negative value is not valid here. 0. (a) : This is an extended Wheatstone's ridge. This is equivalent to X, O, are identical. Three resistances are in parallel connection between and and three more between and., O, have the same potential. The total resistance is + = (d) : 1 The current is the same as 1 and are in series. s 1 < (because 1 is thicker), V is less than V. Therefore E 1 < E where E 1 and E are the fields. (a) is not correct as the areas of cross-section of and are different.. (d) : is only a connecting wire between and which has negligible The current passes from to. 3. (a) : This is a Wheatstone's bridge. There is no current along or. and are in series and and are in series. The equivalent value is = 4. First, one has to mark the points. E This is a Wheatstone's bridge. There is no current through. E mm 7 physics for you February 11 Page 7

Chapter 21 Electric Current and Direct- Current Circuits

Chapter 21 Electric Current and Direct- Current Circuits Units of Chapter 21 Electric Current Resistance and Ohm s Law Energy and Power in Electric Circuits Resistors in Series and Parallel Kirchhoff s