Test 6 Problem 169: EE Board October 1998 A magnetic coil produces produces 100, 100, 000 maxells maxells it! it! ", 000 turns and and it! a current o# "A$ T!e current is cut % o## and t!e #lux collapses in 0$01 sec$ &!at is t!e a'erage 'oltage t!at appear across t!e coil( A$ B$ +$ $
"0 )* "00 * ", 000 000 )* " )*
Problem 1-0: EE Board October 1998 A magnet, !ic! !ic! generates generates 800 800 maxells maxells o# #lux, #lux, is inserted inserted t!roug! t!roug! a coil coil o# 1000 turns$ .t is it!dran it!in 0$1/ sec$ &!at is t!e 'oltage t!at appears across t!e coil( A$ B$ +$ $
0$"" * /$ * / * 0$0/ $0/ *
Problem 1-1: T!e armature coil o# a generator it! /0 conductors on it rotates in a magnetic #ield it! a magnetic #lux densit 1$/ T$ T!e e##ecti'e area o# t!e coil is 1000 s2uare cm$ .# t!is coil is mo'e across t!e pole in 0$/ sec, determine t!e a'erage em# induced in t!e coil$ A$ B$ +$ $
"0 * 1/ * 10 * 1" *
Problem 1-": EE Board April 199 A conductor, conductor, /0 mm long, long, mo'es at at 'elocit 'elocit o# "$/ meters per per second second across a " magnetic #ield o# 0$90 &b3m , &!at is t!e 'oltage generated( A$ B$ +$ $
0$1"/ * 0$06 $0648 * 0$1 0$11"/ * 0$0-" *
Problem 1-: An airplane airplane tra'els tra'els at a speed speed o# 1000 )p! in a region region !ere !ere t!e eart!5s eart!5s magnetic magnetic / #ield is /$0 x 10 T and is nearb 'ertical$ &!at is t!e potential di##erence induced beteen t!e ing tips o# t!e airplane, !ic! is "0 m apart(
A$ B$ +$ $
0$"8 * 0$" * 0$6 * 0$1/ *
Problem 1-4: EE Board October 1998 A piece o# conductor 10 cm long mo'es across a magnetic #ield o# 10, 000 gauss at a 'elocit o# 1"0 cm3sec3 &!at 'oltage appears across t!e conductor( A$ B$ +$ $
0$"4 * 0$1" * 60 * 1"0 *
Problem 1-/: A conductor /0 cm in lengt! mo'es at an angle o# 0 0 to t!e direction o# a magnetic #ield it! a 'elocit o# 100 cm3s$ .# t!e #ield !as a #lux densit o# " &b3m A$ B$ +$ $
"
0$/ * "$0 * 1$0 * 1$/ *
Problem 1-6: A metal dis) o# 0 cm radius rotates at an angular 'elocit o# 1"00 rpm across a uni#orm 'ertical magnetic #ield o# #lux densit 0$/ b3m "$ +alculate t!e 'oltage induced beteen t!e rim and t!e center o# t!e dis)$ A$ B$ +$ $
4$- * /$8 * /$1 * 4$4 *
Problem 1--: A conducting dis) "0 % cm in diameter pi'oted b a 'ertical spindle in !ic! is ling in uni#orm 'ertical magnetic #ield o# #lux densit 0$ T$ A #ixed brus! is connected at t!e edge o# t!e disc$ &!en a 4 resistance is connected across t!e brus! and t!e spindle, a current o# 1/ mA as obser'ed to #lo t!roug! t!e resistor$ etermine t!e 'elocit in !ic! t!e disc is rotating$ A$ B$ +$ $
94 rpm 8" rpm 0" rpm ""8 rpm
Problem 1-8: 7o muc! is t!e inductance o# a coil t!at induces /00 * !en t!e current c!anges t!e rate o# / mA in " us( A$ B$ +$ $
1"$/ u7 0$" 7 0$1 7 " m7
Problem 1-9: T!e #ield inding o# a + generator is ound it! 900 turns and !as a resistance o# /0 o!ms$ .# t!e inding is excited #rom "40 * dc source, t!e magnetic #lux lin)ing coil is 4 m&b$ etermine t!e sel# inductance o# t!e coil$ A$ B$ +$ $
0$-/ 7 0$8 7 0$9" 7 0$/6 7
Problem 180: A coil o# 1000 tums is uni#orml ound on a ring o# non magnetic material, t!e mean diameter being "0 cm$ T!e cross sectional area o# t!e coil is 4 s2uare cm$ etermine t!e sel# inductance o# t!e coil$ A$ B$ +$ $
0$- m7 0$9m7 0$6 m7 0$8 m7
Problem 181: An iron core 0$4 m long and / s2uare cm$ .n cross section, is ound it! 00 turns$ &!en a current o# 0$/ A #los in t!e coil, !o muc! is t!e inductance o# t!e coil$ Assume t!e core !as a permeabilit o# "/00$ A$ B$ +$ $
0$/ 7 0$4" 7 0$"6 7 0$1 7
Problem 18": EE Board October 1990 &!at is t!e coe##icient o# coupling o# to coils !ose mutual inductance is 1 7 and !ose sel# inductance are 1$" and "7( A$ 1$/49 B$ "$400 +$ 0$64/
$ 0$91" Problem 18: A coil o# inductance 8 m7, produces 80 u&b o# magnetic #lux$ O# t!is total #lux 60 u&b are lin)ed to a second coil o# inductance " m7, !o muc! is t!e mutual inductance beteen coils( A$ B$ +$ $
m7 4 m7 / m7 " m7
Problem 184: EE Board April 199" T!e total inductance o# to coils, A and B !en connected in series aiding is 0$/ 7 and 0$" 7 !en connected in series opposing$ +oil A !en isolated #rom coil B !as a sel# inductance o# 0$" 7$ +alculate t!e sel# inductance o# +oil B3 A$ B$ +$ $
0$16 7 0$1" 7 0$"0 7 0$1/ 7
Problem 18/: To identical coils it! sel# inductance o# "/0 u7 eac! are connected in series$ &!en connected series aiding, t!e e2ui'alent inductance is //0 u7 and 4/0 u7 !en connected series opposing, 7o muc! is t!e coupling coe##icient o# to coils( A$ B$ +$ $
0$" 0$ 0$1 0$4
Problem 186: A clinder !ose radius is " cm and altitude o# 100 cm$ is uni#orml ound it! "/00 turns o# ires in a single laer$ A second laer o# 100 turns and o# muc! #iner ires is ound o'er t!e #irst near its center$ +alculate t!e mutual inductance o# t!e to coils$ A$ B$ +$ $
0$40 m7 0$8 m7 0$/" m7 0$6 m7
Problem 18-:
To coils !a'e "00 and 00 turns respecti'el are ound side b side on a common closed core !ose cross section is 100 cm " and mean lengt! o# "00 cm$ &!at ill be t!e 'oltage induced in t!e second coil i# t!e current in t!e #irst coil c!anges #rom 0 to / A in 0$0/ second$ Assume relati'e permitti'it o# t!e core to be 1/00$ A$ B$ +$ $
/"$ * 6-$8 * 6"$6 * /8$6 *
Problem 188: EE Board October 1996 T!e energ &o stored in a coil is dependent in t!e inductance o# t!e coil and t!e current #loing$ .# t!e inductance ere doubled it! t!e same current #loing, !at ould be t!e resulting stored energ( A$ B$ +$ $
"$0 &o 0$/ &o 1$0 &o 4$0 &o
Problem 189: EE Board October 1990 A 6$0 7 coil !ose resistance is 1" o!ms is connected in series it! a "4 o!ms resistor and to a 144 * batter and a sitc!$ T!e sitc! is closed at t ; 0$ etermine t!e energ stored in t!e magnetic #ield at t!e stead state3 A$ B$ +$ $
/0 < 48 < /" < 46 <
Problem 190: To coils !a'ing sel# inductance and mutual inductance o# 7, "7, and 17 respecti'el are connected in series$ .# a current o# 4 A is passed t!roug! t!e coil, e'aluate t!e ratio o# t!e energ stored in t!e magnetic #ield !en t!e #luxes sel# and mutual are in t!e same direction to t!e energ stored !en t!e said #luxes are against eac! ot!er$ A$ B$ +$ $
$"4 "$ 1$- "$6-
Problem 191: EE Board April 199/
To coils o# inductances 4 and 6 !enr are connected in parallel$ .# t!eir mutual inductance is !enr, calculate t!e e2ui'alent inductance o# t!e combination i# mutual inductance assists and i# mutual inductance opposes t!e sel# inductance respecti'el$ A$ B$ +$ $
$4 7 = 1$4 7 $-/ 7 = 0$94 7 6$"/ 7 = "$-/ 7 16 7 = 4 7
Problem 19": A /0 % m7 inductor is c!arged to store 1 < o# energ$ .# an unc!arged 0 m7 inductor is connected across its terminal, !o muc! energ is trans#erred to t!e second inductor( A$ B$ +$ $
0$1/4 < 0$"6" < 0$"4 < 0$141 <
Problem 19: A solenoid /00 cm long and 10 cm in diameter is ound it! 1/00 turns$ >ind t!e energ stored in t!e magnetic #ield !en a current o# / A #los$ A$ B$ +$ $
0$4/ < 0$// < 0$46 < 0$-" <
Problem 194: A coil o# "/0 turns is ound on a close iron ring !ose cross sectional area is "0 " cm and mean lengt! o# 100 cm$ etermine t!e energ stored in t!e magnetic #ield i# a current o# " A is passed t!roug! it$ Assume t!e permeabilit o# iron is 900$ A$ B$ +$ $
"$8 < $1" < "$0 < 1$88 <
