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Page 1 6. E I R r = + ( ) Case I E r = + 0.5 3.75 ( ) Case II E r = + 0.4 (4.75 ) On solving r = 0.25 W, E = 2 V 7. I I g = 50 20 Þ I I g = 5 2 S I I I G g g = - Þ G I I I S g g = - = ´ 3 2 12 = 18 W 8. I I I g = = 2 1 50 % S I I I G G g g = - = 49 9. P V R = 2 P P V R R + = + D D 2 As R l µ DR R = -10% DP V R V R = - 2 2 0.9 = - æ è ç ö ø ÷ 1 1 0.9 P = » 10 9 11 P P % 10. Potential difference between any two points is zero. 11. r l l l R = - 1 2 2 = - ´ 75 60 60 10 =2.5W 12. (b) By ap ply ing KCL at O I I I 1 2 3 0 + + = 6 6 3 3 2 2 0 0 0 0 - + - + - = V V V Þ 6 2 3 3 2 0 0 0 0 - + - + - = V V V ( ) ( ) V 0 3 = V 13. v I neA I ne r d = = p 2 v I ne r v v d d ¢ = = = 2 2 2 2 2 p( ) 14. Voltmeter has higher resistance than ammeter. Again higher the range of voltmeter, higher will be its resistance. 15. I R R R R I 2 2 1 2 3 1 1 1 1 = + + Þ 1 1 1 1 2 2 2 3 R I I R R R = - + æ è ç ç ö ø ÷ ÷ = ´ - + æ è ç ö ø ÷ 0.8 0.3 20 1 20 1 15 = 1 60 R 1 60 = W 16. (d) I E R R A V 1 = + , V I R V 1 1 = = - E I R A 1 If resistance is connected in parallel with voltmeter, 18 A I 1 I I 3 I 2 R=15W 3 R=20W 2 R 1 A B I 2 I 1 3W 6W V 0 O 2W I 3 C A V I 1 E Page 2 6. E I R r = + ( ) Case I E r = + 0.5 3.75 ( ) Case II E r = + 0.4 (4.75 ) On solving r = 0.25 W, E = 2 V 7. I I g = 50 20 Þ I I g = 5 2 S I I I G g g = - Þ G I I I S g g = - = ´ 3 2 12 = 18 W 8. I I I g = = 2 1 50 % S I I I G G g g = - = 49 9. P V R = 2 P P V R R + = + D D 2 As R l µ DR R = -10% DP V R V R = - 2 2 0.9 = - æ è ç ö ø ÷ 1 1 0.9 P = » 10 9 11 P P % 10. Potential difference between any two points is zero. 11. r l l l R = - 1 2 2 = - ´ 75 60 60 10 =2.5W 12. (b) By ap ply ing KCL at O I I I 1 2 3 0 + + = 6 6 3 3 2 2 0 0 0 0 - + - + - = V V V Þ 6 2 3 3 2 0 0 0 0 - + - + - = V V V ( ) ( ) V 0 3 = V 13. v I neA I ne r d = = p 2 v I ne r v v d d ¢ = = = 2 2 2 2 2 p( ) 14. Voltmeter has higher resistance than ammeter. Again higher the range of voltmeter, higher will be its resistance. 15. I R R R R I 2 2 1 2 3 1 1 1 1 = + + Þ 1 1 1 1 2 2 2 3 R I I R R R = - + æ è ç ç ö ø ÷ ÷ = ´ - + æ è ç ö ø ÷ 0.8 0.3 20 1 20 1 15 = 1 60 R 1 60 = W 16. (d) I E R R A V 1 = + , V I R V 1 1 = = - E I R A 1 If resistance is connected in parallel with voltmeter, 18 A I 1 I I 3 I 2 R=15W 3 R=20W 2 R 1 A B I 2 I 1 3W 6W V 0 O 2W I 3 C A V I 1 E I E R RR R R I A V V 2 1 = + + > and V E I R V A 2 2 1 = - < 17. Be fore con nec tiv ity re sis tance is par al lel with ammeter I E R R A V 1 = + , V I R V 1 1 = = - E I R A 1 After connecting resistance in parallel to the ammeter. I E R R A V 2 2 = + , Reading of ammeter = 1 2 2 I = + > E R R I A V 2 1 2 1 V I R E R R V V A V = = + < 2 1 2 2 2 18. R R n e = 2 P V R = 2 P V R n P e e = = 2 2 19. As bulb A is in se ries with en tire cir cuit. 20. I E E R r r R = + + + = + 1 2 1 2 18 3 V E Ir ab = - = 2 2 0 3 18 3 1 0 - + ´ = R Þ R = 3 W 21. I R R R I V 2 = + V R R R R I V V = + 100 2500 2500 5 = + R R R R + = 2500 125 R = 2500 24 W »100W 22. 23. R R 1 2 20 80 1 4 = = …(i) R R 1 2 15 40 60 2 3 + = = 19 V A I 2 I 1 R I R/n R/n R/n A V I 2 E R A V A I 1 E R/10 R/10 R/10 R/10 R/10 R/10 R/10 R/10 R/10 R/10 ß R/5 R/5 R/5 R/5 R/5 Þ R/25 V A I 2 E R Page 3 6. E I R r = + ( ) Case I E r = + 0.5 3.75 ( ) Case II E r = + 0.4 (4.75 ) On solving r = 0.25 W, E = 2 V 7. I I g = 50 20 Þ I I g = 5 2 S I I I G g g = - Þ G I I I S g g = - = ´ 3 2 12 = 18 W 8. I I I g = = 2 1 50 % S I I I G G g g = - = 49 9. P V R = 2 P P V R R + = + D D 2 As R l µ DR R = -10% DP V R V R = - 2 2 0.9 = - æ è ç ö ø ÷ 1 1 0.9 P = » 10 9 11 P P % 10. Potential difference between any two points is zero. 11. r l l l R = - 1 2 2 = - ´ 75 60 60 10 =2.5W 12. (b) By ap ply ing KCL at O I I I 1 2 3 0 + + = 6 6 3 3 2 2 0 0 0 0 - + - + - = V V V Þ 6 2 3 3 2 0 0 0 0 - + - + - = V V V ( ) ( ) V 0 3 = V 13. v I neA I ne r d = = p 2 v I ne r v v d d ¢ = = = 2 2 2 2 2 p( ) 14. Voltmeter has higher resistance than ammeter. Again higher the range of voltmeter, higher will be its resistance. 15. I R R R R I 2 2 1 2 3 1 1 1 1 = + + Þ 1 1 1 1 2 2 2 3 R I I R R R = - + æ è ç ç ö ø ÷ ÷ = ´ - + æ è ç ö ø ÷ 0.8 0.3 20 1 20 1 15 = 1 60 R 1 60 = W 16. (d) I E R R A V 1 = + , V I R V 1 1 = = - E I R A 1 If resistance is connected in parallel with voltmeter, 18 A I 1 I I 3 I 2 R=15W 3 R=20W 2 R 1 A B I 2 I 1 3W 6W V 0 O 2W I 3 C A V I 1 E I E R RR R R I A V V 2 1 = + + > and V E I R V A 2 2 1 = - < 17. Be fore con nec tiv ity re sis tance is par al lel with ammeter I E R R A V 1 = + , V I R V 1 1 = = - E I R A 1 After connecting resistance in parallel to the ammeter. I E R R A V 2 2 = + , Reading of ammeter = 1 2 2 I = + > E R R I A V 2 1 2 1 V I R E R R V V A V = = + < 2 1 2 2 2 18. R R n e = 2 P V R = 2 P V R n P e e = = 2 2 19. As bulb A is in se ries with en tire cir cuit. 20. I E E R r r R = + + + = + 1 2 1 2 18 3 V E Ir ab = - = 2 2 0 3 18 3 1 0 - + ´ = R Þ R = 3 W 21. I R R R I V 2 = + V R R R R I V V = + 100 2500 2500 5 = + R R R R + = 2500 125 R = 2500 24 W »100W 22. 23. R R 1 2 20 80 1 4 = = …(i) R R 1 2 15 40 60 2 3 + = = 19 V A I 2 I 1 R I R/n R/n R/n A V I 2 E R A V A I 1 E R/10 R/10 R/10 R/10 R/10 R/10 R/10 R/10 R/10 R/10 ß R/5 R/5 R/5 R/5 R/5 Þ R/25 V A I 2 E R R R R 1 2 2 15 2 3 + = 15 2 3 1 4 5 12 2 R = - = Þ R 2 36 = W, R R 1 2 4 9 = = W 24. (b) As V V 1 2 = , R R 1 2 = R R V V ´ + = 100 100 50 R V = 100 W 25. (d) E R r PB + = + = 2 4 1 0.4 W V IR AB AB = = 1.6 W K V L PB = = = 1.6 0.016 100 V/cm L E K = = = 1 75 1.2 0.016 cm 26. (d) V AB = ´ + + ´ - + ´ 3 2 3 1 4 2 6 1 =17 V 27. (c) E E r E r r r e = + + = 1 2 2 1 1 2 2 V r r r r r e = + = 1 2 1 2 0.5 W For maximum power R r e = and P E r e e max ( ) = = ´ = 2 2 4 2 4 2 0.5 W 28. (a) V R R r E = + r E V R = - æ è ç ö ø ÷ = - æ è ç ö ø ÷ 1 1 5 2.2 1.8 = 10 9 W 29. (d) I E E R R r r = - + + + 1 2 1 2 1 2 = - + + + 10 5 25 15 2.5 2.5 = 1 9 A V I AB = - + ( ) 25 15 = - ´ » - 1 9 40 4 V 30. (a) V kL AB = = ´ 0.2 100 = 20 mV V R R R E AB AB AB = + Þ 0.02 = + ´ R R AB AB 490 2 Þ R R AB AB + = 490 100 R AB = » 490 99 4.9W 31. (c) When key is open, I E R 1 2 3 = When key is closed I E R 2 3 4 = \ I I 1 2 8 9 = 20 2W 2W 1W 1W 2W 2W A 3V 2V B 3A 1A 2A A E I 1 R 2R 2R R Þ A E 3R 3R I 1 ß A E 3R 3/2R I 1 A E I 2 R 2R 2R R Þ A E I 2 ß A 4R/3 I 2 2R/3 2R/3 Page 4 6. E I R r = + ( ) Case I E r = + 0.5 3.75 ( ) Case II E r = + 0.4 (4.75 ) On solving r = 0.25 W, E = 2 V 7. I I g = 50 20 Þ I I g = 5 2 S I I I G g g = - Þ G I I I S g g = - = ´ 3 2 12 = 18 W 8. I I I g = = 2 1 50 % S I I I G G g g = - = 49 9. P V R = 2 P P V R R + = + D D 2 As R l µ DR R = -10% DP V R V R = - 2 2 0.9 = - æ è ç ö ø ÷ 1 1 0.9 P = » 10 9 11 P P % 10. Potential difference between any two points is zero. 11. r l l l R = - 1 2 2 = - ´ 75 60 60 10 =2.5W 12. (b) By ap ply ing KCL at O I I I 1 2 3 0 + + = 6 6 3 3 2 2 0 0 0 0 - + - + - = V V V Þ 6 2 3 3 2 0 0 0 0 - + - + - = V V V ( ) ( ) V 0 3 = V 13. v I neA I ne r d = = p 2 v I ne r v v d d ¢ = = = 2 2 2 2 2 p( ) 14. Voltmeter has higher resistance than ammeter. Again higher the range of voltmeter, higher will be its resistance. 15. I R R R R I 2 2 1 2 3 1 1 1 1 = + + Þ 1 1 1 1 2 2 2 3 R I I R R R = - + æ è ç ç ö ø ÷ ÷ = ´ - + æ è ç ö ø ÷ 0.8 0.3 20 1 20 1 15 = 1 60 R 1 60 = W 16. (d) I E R R A V 1 = + , V I R V 1 1 = = - E I R A 1 If resistance is connected in parallel with voltmeter, 18 A I 1 I I 3 I 2 R=15W 3 R=20W 2 R 1 A B I 2 I 1 3W 6W V 0 O 2W I 3 C A V I 1 E I E R RR R R I A V V 2 1 = + + > and V E I R V A 2 2 1 = - < 17. Be fore con nec tiv ity re sis tance is par al lel with ammeter I E R R A V 1 = + , V I R V 1 1 = = - E I R A 1 After connecting resistance in parallel to the ammeter. I E R R A V 2 2 = + , Reading of ammeter = 1 2 2 I = + > E R R I A V 2 1 2 1 V I R E R R V V A V = = + < 2 1 2 2 2 18. R R n e = 2 P V R = 2 P V R n P e e = = 2 2 19. As bulb A is in se ries with en tire cir cuit. 20. I E E R r r R = + + + = + 1 2 1 2 18 3 V E Ir ab = - = 2 2 0 3 18 3 1 0 - + ´ = R Þ R = 3 W 21. I R R R I V 2 = + V R R R R I V V = + 100 2500 2500 5 = + R R R R + = 2500 125 R = 2500 24 W »100W 22. 23. R R 1 2 20 80 1 4 = = …(i) R R 1 2 15 40 60 2 3 + = = 19 V A I 2 I 1 R I R/n R/n R/n A V I 2 E R A V A I 1 E R/10 R/10 R/10 R/10 R/10 R/10 R/10 R/10 R/10 R/10 ß R/5 R/5 R/5 R/5 R/5 Þ R/25 V A I 2 E R R R R 1 2 2 15 2 3 + = 15 2 3 1 4 5 12 2 R = - = Þ R 2 36 = W, R R 1 2 4 9 = = W 24. (b) As V V 1 2 = , R R 1 2 = R R V V ´ + = 100 100 50 R V = 100 W 25. (d) E R r PB + = + = 2 4 1 0.4 W V IR AB AB = = 1.6 W K V L PB = = = 1.6 0.016 100 V/cm L E K = = = 1 75 1.2 0.016 cm 26. (d) V AB = ´ + + ´ - + ´ 3 2 3 1 4 2 6 1 =17 V 27. (c) E E r E r r r e = + + = 1 2 2 1 1 2 2 V r r r r r e = + = 1 2 1 2 0.5 W For maximum power R r e = and P E r e e max ( ) = = ´ = 2 2 4 2 4 2 0.5 W 28. (a) V R R r E = + r E V R = - æ è ç ö ø ÷ = - æ è ç ö ø ÷ 1 1 5 2.2 1.8 = 10 9 W 29. (d) I E E R R r r = - + + + 1 2 1 2 1 2 = - + + + 10 5 25 15 2.5 2.5 = 1 9 A V I AB = - + ( ) 25 15 = - ´ » - 1 9 40 4 V 30. (a) V kL AB = = ´ 0.2 100 = 20 mV V R R R E AB AB AB = + Þ 0.02 = + ´ R R AB AB 490 2 Þ R R AB AB + = 490 100 R AB = » 490 99 4.9W 31. (c) When key is open, I E R 1 2 3 = When key is closed I E R 2 3 4 = \ I I 1 2 8 9 = 20 2W 2W 1W 1W 2W 2W A 3V 2V B 3A 1A 2A A E I 1 R 2R 2R R Þ A E 3R 3R I 1 ß A E 3R 3/2R I 1 A E I 2 R 2R 2R R Þ A E I 2 ß A 4R/3 I 2 2R/3 2R/3 32. (b) S I I I G g g = - = ´ 1 34 33 34 3663 I I = 111 W R r e = 5 11 r = ´ 11 5 1.5 = 3.3 W As the circuit is symmetrical about perpendicular bisector of AB, all points lying on it are at same potential. 35. (c) R L L L R 1 1 1 2 = + Þ R R 1 6 3 = = W R l l l 2 2 1 2 = + Þ R 2 15 = W Hence R 1 and R 2 are in parallel R R R R R e = + 1 2 1 2 = 2.5W 36. (c) Let R R x AD BC = = Clearly x < 1 as 1W resistor is in parallel with some combination. Now R x x AB = + + 1 = + 2 1 x As x < 1 1 3 < < R AB 37. (d) R R R R R R R R AB = + + + = ( ) 0 0 0 2 Þ 2 2 2 0 2 0 0 0 2 R RR R RR RR R + + + = + Þ 3 2 0 2 R R = Þ R R = 0 3 38. 21 33. B A r r r r r r r r r r r r r r 2r B A Þ ß A B r r 2r/3 2r/3 r A B Þ 5/3r 5/3r r ß 5/11r 2r (b) 34. r r r r r r r r r r A B Þ r r r r r r r r A ß B 2r 2r 2r 2r B A Þ B A r/2 (b) R 2 R 1 a b 60° 1W 1W 1W 1W 1W 1W 1W 1W 1W 1W 1W 1W 1W B A P Q R R R R Þ P Q R R/2 R/3 ß P Q R 5 11 R Ü 5 6 R = 25W R R Page 5 6. E I R r = + ( ) Case I E r = + 0.5 3.75 ( ) Case II E r = + 0.4 (4.75 ) On solving r = 0.25 W, E = 2 V 7. I I g = 50 20 Þ I I g = 5 2 S I I I G g g = - Þ G I I I S g g = - = ´ 3 2 12 = 18 W 8. I I I g = = 2 1 50 % S I I I G G g g = - = 49 9. P V R = 2 P P V R R + = + D D 2 As R l µ DR R = -10% DP V R V R = - 2 2 0.9 = - æ è ç ö ø ÷ 1 1 0.9 P = » 10 9 11 P P % 10. Potential difference between any two points is zero. 11. r l l l R = - 1 2 2 = - ´ 75 60 60 10 =2.5W 12. (b) By ap ply ing KCL at O I I I 1 2 3 0 + + = 6 6 3 3 2 2 0 0 0 0 - + - + - = V V V Þ 6 2 3 3 2 0 0 0 0 - + - + - = V V V ( ) ( ) V 0 3 = V 13. v I neA I ne r d = = p 2 v I ne r v v d d ¢ = = = 2 2 2 2 2 p( ) 14. Voltmeter has higher resistance than ammeter. Again higher the range of voltmeter, higher will be its resistance. 15. I R R R R I 2 2 1 2 3 1 1 1 1 = + + Þ 1 1 1 1 2 2 2 3 R I I R R R = - + æ è ç ç ö ø ÷ ÷ = ´ - + æ è ç ö ø ÷ 0.8 0.3 20 1 20 1 15 = 1 60 R 1 60 = W 16. (d) I E R R A V 1 = + , V I R V 1 1 = = - E I R A 1 If resistance is connected in parallel with voltmeter, 18 A I 1 I I 3 I 2 R=15W 3 R=20W 2 R 1 A B I 2 I 1 3W 6W V 0 O 2W I 3 C A V I 1 E I E R RR R R I A V V 2 1 = + + > and V E I R V A 2 2 1 = - < 17. Be fore con nec tiv ity re sis tance is par al lel with ammeter I E R R A V 1 = + , V I R V 1 1 = = - E I R A 1 After connecting resistance in parallel to the ammeter. I E R R A V 2 2 = + , Reading of ammeter = 1 2 2 I = + > E R R I A V 2 1 2 1 V I R E R R V V A V = = + < 2 1 2 2 2 18. R R n e = 2 P V R = 2 P V R n P e e = = 2 2 19. As bulb A is in se ries with en tire cir cuit. 20. I E E R r r R = + + + = + 1 2 1 2 18 3 V E Ir ab = - = 2 2 0 3 18 3 1 0 - + ´ = R Þ R = 3 W 21. I R R R I V 2 = + V R R R R I V V = + 100 2500 2500 5 = + R R R R + = 2500 125 R = 2500 24 W »100W 22. 23. R R 1 2 20 80 1 4 = = …(i) R R 1 2 15 40 60 2 3 + = = 19 V A I 2 I 1 R I R/n R/n R/n A V I 2 E R A V A I 1 E R/10 R/10 R/10 R/10 R/10 R/10 R/10 R/10 R/10 R/10 ß R/5 R/5 R/5 R/5 R/5 Þ R/25 V A I 2 E R R R R 1 2 2 15 2 3 + = 15 2 3 1 4 5 12 2 R = - = Þ R 2 36 = W, R R 1 2 4 9 = = W 24. (b) As V V 1 2 = , R R 1 2 = R R V V ´ + = 100 100 50 R V = 100 W 25. (d) E R r PB + = + = 2 4 1 0.4 W V IR AB AB = = 1.6 W K V L PB = = = 1.6 0.016 100 V/cm L E K = = = 1 75 1.2 0.016 cm 26. (d) V AB = ´ + + ´ - + ´ 3 2 3 1 4 2 6 1 =17 V 27. (c) E E r E r r r e = + + = 1 2 2 1 1 2 2 V r r r r r e = + = 1 2 1 2 0.5 W For maximum power R r e = and P E r e e max ( ) = = ´ = 2 2 4 2 4 2 0.5 W 28. (a) V R R r E = + r E V R = - æ è ç ö ø ÷ = - æ è ç ö ø ÷ 1 1 5 2.2 1.8 = 10 9 W 29. (d) I E E R R r r = - + + + 1 2 1 2 1 2 = - + + + 10 5 25 15 2.5 2.5 = 1 9 A V I AB = - + ( ) 25 15 = - ´ » - 1 9 40 4 V 30. (a) V kL AB = = ´ 0.2 100 = 20 mV V R R R E AB AB AB = + Þ 0.02 = + ´ R R AB AB 490 2 Þ R R AB AB + = 490 100 R AB = » 490 99 4.9W 31. (c) When key is open, I E R 1 2 3 = When key is closed I E R 2 3 4 = \ I I 1 2 8 9 = 20 2W 2W 1W 1W 2W 2W A 3V 2V B 3A 1A 2A A E I 1 R 2R 2R R Þ A E 3R 3R I 1 ß A E 3R 3/2R I 1 A E I 2 R 2R 2R R Þ A E I 2 ß A 4R/3 I 2 2R/3 2R/3 32. (b) S I I I G g g = - = ´ 1 34 33 34 3663 I I = 111 W R r e = 5 11 r = ´ 11 5 1.5 = 3.3 W As the circuit is symmetrical about perpendicular bisector of AB, all points lying on it are at same potential. 35. (c) R L L L R 1 1 1 2 = + Þ R R 1 6 3 = = W R l l l 2 2 1 2 = + Þ R 2 15 = W Hence R 1 and R 2 are in parallel R R R R R e = + 1 2 1 2 = 2.5W 36. (c) Let R R x AD BC = = Clearly x < 1 as 1W resistor is in parallel with some combination. Now R x x AB = + + 1 = + 2 1 x As x < 1 1 3 < < R AB 37. (d) R R R R R R R R AB = + + + = ( ) 0 0 0 2 Þ 2 2 2 0 2 0 0 0 2 R RR R RR RR R + + + = + Þ 3 2 0 2 R R = Þ R R = 0 3 38. 21 33. B A r r r r r r r r r r r r r r 2r B A Þ ß A B r r 2r/3 2r/3 r A B Þ 5/3r 5/3r r ß 5/11r 2r (b) 34. r r r r r r r r r r A B Þ r r r r r r r r A ß B 2r 2r 2r 2r B A Þ B A r/2 (b) R 2 R 1 a b 60° 1W 1W 1W 1W 1W 1W 1W 1W 1W 1W 1W 1W 1W B A P Q R R R R Þ P Q R R/2 R/3 ß P Q R 5 11 R Ü 5 6 R = 25W R R 39. Wheatstone bridge is bal anced. Þ R R e = 7 6 40. (d) R L L L R R 1 1 1 2 1 12 = + = = 3 W R L L L R 2 2 1 2 11 12 = + = = 33 W R 1 and R 2 are in parallel, R R R R R e = + = ´ + 1 2 1 2 3 33 3 33 =2.75W 41. (a) Re sis tance per unit length of wire = 4 2pr R r r R 1 2 4 2 2 = ´ = = p p R r r 3 4 2 2 4 = ´ = p p \ 1 1 1 1 1 2 3 R R R R e = + + = + + = + 1 2 1 2 4 4 4 p p R e = + 4 4 p W 42. (d) Points C and D are shorted hence the por tion above line CD can be re moved. 43. (b) As AB is line of sym me try, we can fold the network about AB. 22 A B 30° O A R/2 R/2 R/2 R/2 R/2 R/2 B Þ R/2 R/2 B A R R ß 3R/2 A B A R R R 2R/3 2R/3 2R/3 2R/3 Ü P R R R R R R R R R R R R R B B ß Þ Þ 4R/3 4R/3 4R/3 4R/3 7R/3 7R/3 R R R R A B A R R R R R R R R R B R A B R 2 R 3 R 1 D B A C ß D B A C R/2 R/2 R B A Ü R R A B R/2 B A Ü ßRead More
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