CHAP. 3]

31

CIRCUIT LAWS

Fig. 3-11 The two 20-mH inductances have an equivalent inductance of 10 mH. Since this is in parallel with the 10-mH inductance, the overall equivalent inductance is 5 mH. Alternatively, 1 1 1 1 1 1 1 4 þ þ ¼ ¼ þ þ ¼ Leq L1 L2 L3 10 mH 20 mH 20 mH 20 mH

3.6

or

Leq ¼ 5 mH

Express the total capacitance of the three capacitors in Fig. 3-12.

Fig. 3-12 For C2 and C3 in parallel, Ceq ¼ C2 þ C3 . CT ¼

3.7

Then for C1 and Ceq in series,

C1 Ceq C ðC þ C3 Þ ¼ 1 2 C1 þ Ceq C1 þ C2 þ C3

The circuit shown in Fig. 3-13 is a voltage divider, also called an attenuator. When it is a single resistor with an adjustable tap, it is called a potentiometer, or pot. To discover the eﬀect of loading, which is caused by the resistance R of the voltmeter VM, calculate the ratio Vout =Vin for (a) R ¼ 1, (b) 1 M , (c) 10 k , (d) 1 k . ðaÞ

Vout =Vin ¼

250 ¼ 0:100 2250 þ 250

Fig. 3-13

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
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