# Schaum's outline of theory and problems of basic circuit by John O'Malley By John O'Malley

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1 1 What is the length of No. 000 126 in2 in cross-sectional area) Nichrome wire required for a 24-0 resistor at 20°C? 000 126 &)(24\$) X--X-0 . 12 23 RESISTANCE CHAP. 21 A certain aluminum wire has a resistance of 5 R at 20°C. What is the resistance of an annealed copper wire of the same size and at the same temperature'? For the copper and aluminum wires, respectively, R=p,- I 5 and A I pa - = A Taking the ratio of the two equations causes the length and area quantities to divide out. 56 iz. A 100-m length of wire of the same material has a resistance of 2 R at the same temperature.

Consider finding the voltage V,. By Ohm’s law, V, = ZR,. Also, Z = V’/(R, + R , + R 3 ) . Eliminating Z results in In general, for any number of series resistors with a total resistance of RT and with a voltage of Vs across the series combination, the voltage V’ across one of the resistors R , is This is the formula for the voltage division or divider rule. For this formula, Vs and V, must have opposing polarities; that is, around a closed path one must be a voltage drop and the other a voltage rise.

F 4OV I Fie. 3-5 p Fig. 6 SERIES AND PARALLEL DC CIRCUITS [CHAP. 3 Find the unknown voltages in the circuit shown in Fig. 3-7. Find Vl first. The basic KVL approach is to use loops having only one unknown voltage apiece. Such a loop for V, includes the 10-, 8-, and 9-V components. The sum of the voltage drops in a clockwise direction around this loop is 10 - 8 + 9 - V1= 0 from which V, = I 1 v Similarly, for V2 the sum of the voltage drops clockwise around the top mesh is V2 + 8 - 10 = 0 from which V2=2V Clockwise around the bottom mesh, the sum of the voltage drops is -8 + 9 + v, = 0 from which V,= - l v The negative sign for C< indicates that the polarity of the actual voltage is opposite the reference polarity.