> KIRCHHOFF’S RULES 2 In the circuit shown in Fig. 6.43. £, F, Gand H are cells of emis a 2V. IV, 3V and IV yy oth, 20! and their internal 7 resistances are 22, uf 10, 3Q and 10 oe onan i respectively. J Calculate Figure 6.43, (a) pd between B and D and (b)_pdacross the terminals of each of the cells Gand H. ICBSE 03], (Ans. (a) (2/13) V(b) 1.62 V, 1.46 V} Two cells, of emfs 1.5V and 2V and internal resistances 20 and IS2respectively, have their negative terminals joined by a wire of 682 and positive terminals by a wire of 40 resistance. A third wire of 8 resistance connects the middle points of these wires. Draw the circuit diagram, Using Kirchhoff's rule, find the pd at the ends of this third wire. [ese] [Ans. 1.26 V] A single loop contains two extemal resistors and two batteries as shown in Fig. 6.44. (a) Find the current (J) in the circuit (b) What is the power lost in each resistor? [ans (= on FR, = 88 atv Figure 6.44 ©)(8)W, (109)W] Find the currents 7, and J in the circuit shown it Fig. 6.45. Also find the pd between b and c Figure 6.45 3A, 1 SIA yh = 2V] Under steady state conditions, find the unknown curren it the multiple loop circuit shown in Fig, 6.46. What i ccharge on the capacitor? (Ans. 1 = 138A, 1, =-0.364, 1 02A; 66.0 uC}: x Figure 6.47 4, Calculate the pd between the junctions B and D in the Wheatstone bridge shown in Fig. 6.47 {ars 02V] +, Apart of the circuit in a steady state along with the currents flowing in the branches, the values of resistances ete. is shown in Fig. 6.48, Calculate the energy stored in the capacitor. Ans. 810] Figure. 6.46 go sa 50a goof s00 Figure 6.49 Ts Figure 6.48 4. Find the equivalent resistance between the points A and B of the circuit shown in Fig. 6.49. [Ams. 200) > POTENTIOMETER 3. A potentiometer wire of length Im has a resistance of 10082. vis connected in series with a resistance and a battery of ‘emf 2V and of negligible resistance. A source of emf 10mV is balanced against a length of 40 cm of the potentiometer Wire, Whatis the value of the external resistance? [11] {Ans, 7900} ' In a potentiometer, a standard cell of emf SV and of Tegligible resistance, maintains a steady current through the Potentiometer wire of length Sm. Two primary cells of emfs € and €, are joined in series with : (a) same polarity and (b) posite polarities. The combination is connected through a falvanometer and a jockey to the potentiometer. The balancing length inthe two cases are found to be 350 em and 0 cm respectively. (@) Draw the necessary circuit diagram. (©) Find the value of the emfs of the two cells. (Ans. 20V, 150) 4.10 m long wire of uniform cross-section and 2082 resis ‘ance is used as a potentiometer wire. The wire is connected '0 series with a battery of SV, along with an external ICBSEO4] u 14, resistance of 4800. If'an unknown emf € is balanced at 600 em of this wire, calculate (a) the potential gradient of potentiometer wire and ICBSE 06} 2v 150 (b) the value of unknown emfe. Tans. (a) 2510" Viem (b) 0.12 VI ABs | m long uniform wire of 1002 resistance. Other data are shown 1 | fe Fig, 6.50. Calculate (a) potential gradient along AB and (b) length AO when the galvano- meter shows no deflection. [CBSE] (Ans. (a) 8+ 107 Viem (6) 37.5 em} ‘The length of a potentiometer wire is 5 m. Iris connected to a battery of constant emf, For a given Leclanche’ cell, the position of zero galvanometer deflection is obtained at 100 cm. Ifthe length of the wire be ‘made 8 m instead of S m, calculate the length of the wire for zero deflection in the galvanometer for the same cell ICBSE| Figure 6.50 [Ans. 1.6m) A cell gives a balance with 85 om of a potentiometer wire, When the terminals of the cell are shorted through a resistance of 7.50, the balance is obtained at 75 cm. Find the internal resistance of the cell {Ans. 10] > WHEATSTONE BRIDGE AND METRE-BRIDGE 15, 16. 17. Ina Wheatstone bridge, the ratio arms P and Q are approxi- ‘mately equal. When R = 500Q, the bridge is balanced. On interchanging P, the value of R for balancing is 505.9. Find the value of S and ratio PQ. [Ans. 502.5 2, 151.005} In a metre-bridge experiment, a resistor of resistance R is kept in the left gap in all observations. When R; and Rs are connected in tum in the right gap, the balance point is ‘obtained at 60 cm and 50 cm from zero end of the wire. Find the position of the balance point when the right gap contains Ry and Ry : (a) in series and (b) in parallel (Ans. (a) 37.5 em (b) 71.43 em] When two resistance wires are in the two gaps of a metre- bridge, the balance point was found to be (1/3)m trom the zero end, When a 62 coil is connected in series with the smaller of the two resistances, the balance point is shifted to (2/3) m from the same end. Find the resistances of the two wires. [Ans 20,40)