18 Alternating Currents Tutorial

4 ¼ö ß¾ effect (J 8 3 /1/1 0 ) steady culT ent, w hen passed through the sam e resistor, w o u ©¥d have an identical heating T he periodic current passes through a resistor, producing heat at a certain rate. S tate the (©¥©¥) the root - r n e a n - square current. (©¥» the average value of the current, T he figure above show s the variation w ith tim e t of a periodic current I . D eterm ine r r U 1 ï l A «ili) the m axim um power in the resistor. (ii) the m ean pow er in the resistor, (1) the peak value of the culT ent, resistor. ca©¥cu©¥ate A sinusoida©¥ aïtem ating culT ent of r. m . s . v a lue 5 . 0 A passes through a 4 . 0 Q «b» C a©¥culate the peak value of a 2 4 0 V m ains electń city supp©¥y . S P 1 . (a) W nat is m eant by the r. m . s . v a ©¥ue of an a©¥tem ating cu©¥T ent? S e©¥f - P ractice Q uestions 5 7 . E xplain how a diode is used for rectification af an alternating current. and output potential di¨¤erences, a n d the pń m ary and secondary currents? 5 6 . F or an idea©¥ transform er, w hat is the relationship betw een the turns ratio of w indings, the input 5 5 . E xp©¥ain the principle of operation of a sim ple iron - c o r e transform er. 5 4 . W nat is the relationship betw een r. m . s . a n d peak values for a sinusoidal current? a©¥tem ating current. 5 3 . D educe that the m ean pow er in a resistive ©¥oad is half the m axim um pow er for a sinusoidal frequency, peak value and root - m e a n s quare value? 5 2 _ A sinusoidal current is represented by the equation İ = I . s ln (a) t) . W hat is its period, an a©¥tem ating current? 5 1 . W nat is m eant by peń od, frequency, peak value and root - m e a n s quare current as applied to S elf - C heck Q uestions ¡¤

C a©¥cu©¥ate the Y q lat ¢æsensitivity of the c. r. o. 1 . 0 cm 团 团 1¡á国 üÞ国团 团üÞ国 ©¥国©¥国 ìé 为¡¢0 ©¥国ÞÌ国 国©¥©¥ ©¥团 团 1 .o cm îìÒì£üÞ国 1国©¥©¥©¥©¥ 团团¡á©¥üÞ国 国 团团©¥国 ©© ¡¢ ¡£ ß¾üÞ国 团 团©¥国国 is sw itched on . p -d. Is applied to the Y - input. T he r. m . s. v a lue of the applied p . d. Is 4 . 24 V . T he tim e - base T he diagram show s the display on a cathode - ray oscilloscope (c. r . o. ) w hen a sinusoidalS P 6 . (M odified from J 9 3 /0 2 0 ) A ssum ing the transform er is 1 0 0 % efficient, w hat are the m issing entries? 222222222222 .o 11llllllllll团 团 国ÍÝ团 团 国ÍÝ团 团 国 国团 团 国 国团 团 国ÍÝ团 团 国ÍÝ llllllllllll团 团 国ÍÝ团 团 国ÍÝ团 团 国ÍÝ团 团 国 旧团 团 国ÍÝ团 团 国ÍÝ llllllllllll团团团Ï¡üÞ国团团Ï¡üÞ国团团Ï¡üÞ国团团ìíÞÌ国 ÏÐ国 ÏÐ 5o24 0 Vp / v I lp / m A I©¥W t u ÞÌ国 ©¥ K / v /©¥ / m A N ©¥ tu rn s In a ©¥aboratory experim ent to test a transform er, a s tudent obtained the fo©¥©¥ow ing results.S P 5 . across the secondary coil. coil is connected across a variable resistor. S uggest ways in w hich you can decrease the p . d. T he prim ary coil of a transform er is connected to an alternating voltage supply . T he secondaryS P 4 . heater now dissipate energy? (N 2 0 0 0 /1/2 1 ) connected to a 3 4 0 V d. c. supply and its resistance rem ains the sam e. A t w hat rate does the connected to this supply, a heater dissipates energy at a rate of 1 0 0 0 W . T he heater is then S P 3 . A m ains electricity supply has a r. m . s. v o ltage of 2 4 0 V and a peak voltage of 3 4 0 V . W hen

i ¡Æ ¡Æ (b) W hat can you conc©¥ude from your answ ers to (i) arid (ii)? ¡¼1¡½ (i) Oi) D 3 (a) C alculate the r. m . s . c u r r e n t of (i) and (ii) ¡¼2 ¡½ Fig . 2bF ig . 2 a 个 ¡¹ F ig . 2b is applied across the sam e resistor. D eterm ine the m ean rate of heat production w hen the square - w a v e o f potentia©¥ V 2 show n in at a m ean rate p . D 2 . A sinusoidal potential V 1 show n in F ig . 2 a is applied across a resistor R w hich produces heat * (J88/©¥/23) A E A B if the current just exceeds W hen the a. c . supply is replaced with a 1 2 0 V d, c . s o u rce, a n identical fuse breaks the circuit below , the fuse F break W hen an a. c , s u pply of 2 4 0 V r. m . s . le connected to the term inals A B In the circuit shownD 1 . C haracteristics of A ltem etíng C um nts D iscussion Q uestions

4 (d) root - m e an - a qaure value of potential difference [1 ] : i)i\ l, (c) peak value of potential di¨¤erence, ¡¼1¡½ following quantities : W F or the alternating potential difference applied to the Y - plates, deduce the values of the ― ― deflection is 0 . 50 m s cm ¡¤ 1 . T he Y - plate sensitivity is set at 2 . 0 V cm 1 and the tim ebase is set so that the horizontal 售 ©¥ üÞ国©¥国©¥国园 ©¥¡á电×ì国ÍÝ©¥ IüÞ国 \l/ I I \ ÙÍÍÝ国©¥ª·国ÍÝä¹ìé I Ú¶ÙÍ国ÙÍ©¥¡¸¡¤旧 崮 ÍÝ1 阳ÙÍÏ¡ê®园øÕ ー ªË ー üÞ©¥©¥ÙÍ团 团©¥ªË ¡á ©¥©¥ = ©¥ = ©¥©¥ ©¥©¥©¥ l= ©¥ ©¥©¥©¥ screen is as show n below . T he squares on the screen have sides of one centim etre. D 4 . A cathode - r a y oscilloscope (c. r . o. ) is connected across the output of a transform er and the (c) D eterm ine the r. m . s . c u r r e n t of (iii) and (lv) [4 ]

C D lls th respect to z? W hich one of the graphs best represents the corresponding variation of the potential of X w ith ¡Æm d tinn ų , É X G X " , rwt . T he graph below show s the variationD 8 .D 8 . D R oot - m ean - s quare vo©¥tage across resistor R is ha©¥f of the peak voltage applied across it. the stages w hen the diode is reverse - biased. C T he tim e intervals corresponding to zero voltage across resistor R in the graph represent B T he period of the V R - tgraph is half of that of the V s - tgraph. directional. A H alf - w a v e r e c tification takes place so that the current supp©¥ied to the resistor ls one - W hich of the fo©¥low ing statem ents is incotT ecť? ¡¤ ' . , . diagram . tim e t variation of the supply voltage V a and the p . d. Vn across the ree©¥stor are show n in the D 7 . A n a©©ternating supply ia applĺed to a resistor R w ith a diode connected ©¥n series with It, T he R ectification . Q

(J20007©¥1/5) (©¥i) S uggest why the resistor ls necessary ©¥n the circuit [1 ] (i) S uggest why the diode is necessary in the secondary circuit [1 ] (b) T he switch ía now closed so that the battery ©¥s being recharged. (©¥l¡· the peak potentia! di¨¤erence across the secondary ¡¼1 ¡½ (i) the r. m . s . potential di¨¤erence across the secondary, ¡¼1¡½ calculate (a) Initia©¥ly the sw itch is open. C onsidering both the transform er and the diode to be idea©¥, 2 30 V r. m . s 9 . 0 V rechaeab©¥e battery, a s illustrated in the figure below . T he secondary coi©¥ has 4 0 turns and m ay be connected, through a sw itch and a diode, to a The ¨¤im ary coil of a transform er has 1 0 0 0 turns and is connected to a 2 3 0 V r. m . s . s u pp©¥y . D 6 . ' " da¡¸y ÏÐüÞ国国 ¡£ dissipated in the resistoť ? W nat are possible values of the secondary voltage, the secondary current and tt©¥e m ean power 15 V 12 0 0 diagram . secondary has 3 2 0 0 h©¥m s and is cat©¥ned ed ©¥o a resistor of resistance 1 2 0 a as sho*m in tt©¥e T he p a r y af an ideal transformer has 2 0 0 hm s and iB conned ed to a 1 5 V supp©¥y - T heD 5 . T he transfo rm er

C D 1 . C S P 6 , 2 . 0 V cm - 1 S P 5 . 12 50 , 9 . 6 V S P 3 , 2000 W S P 2 . 1 . 0 A , 2 . 0 A , 2 . 0 A A n©¥ S P 1 . 339 V , 7 . 0 7 A , 100 W , 200 W D eterm ine the r. m . s. c u r r e n t show n in the figure, (R JC 2004 P re©¥im P 1 Q 2 3 ) * K n o w ©¥e d ge of m utual inductance is required in this question. is the num ber of turns per unit length and İ is the current in the solenoid. ] [M agneüc flux density in a solenoid, B _ / ©¥ o n l w here J©¥o is the pe rm eability of fre e spa ce , n at 2 . 0 A 5 1 is then sent through Q . W hat e. m . f. w i©¥i be induced in P ? induced in Q . T he current in P is then sw itched off. In F ig . 2 3 . 2 , a c u rr e n t w hich is changing ©¥n F ig . 2 3 . 1 , w hen the current in P changes at a rate of 5 . 0 A s ' 1 , a n e. m . f. o f 2 . 0 m v is C 2 . * n 2 32 N = 1 0 N a 6 0 P Q 10 and 5 0 turns respectively .