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The circuit to be analyzed is Fig. 6-16 with a resistor RE connected from E to C. With terminal pair B; C open, the voltage across terminals C; E is zero; thus, the Thevenin equivalent circuit consists only of ZTh RTh . Now consider vbc as a driving-point source, and apply KVL around the B; C loop to obtain vdp vbc hic ib hrc vec % hic ib vec Use KCL at node E to obtain vec ie RE hfc ib hoc vce RE % hfc RE ib Substitute (2) into (1), and solve for the driving-point impedance: RTh vbc hic hfc RE ib 3 2 1

Now (3) is compared with (6.16), it becomes apparent that hic hie and hfc hfe 1 , as given in (3) of Problem 6.14.

1 4 4 3 (2) (2) + 2(2)2 4 3

Apply the de nitions of the general h parameters given by (1.16) to (1.19) to the circuit of Fig. 6-1(b) to determine the CE h parameters in terms of the CB h parameters. Use the typically good approximations hrb ( 1 and hob hib ( 1 hfb to simplify the results.

As discussed previously, the worksheet is usually prepared in pencil on a multicolumn sheet of accounting stationery called analysis paper. On the worksheet, the ledger accounts are adjusted, balanced, and arranged in proper form for preparing nancial statements. All procedures can be re viewed quickly, and the adjusting and closing entries can be made in the formal records with less chance of error. Moreover, with the data for the income statement and balance sheet already proved out on the worksheet, these statements can be prepared more readily. For a typical merchandise business, we may suppose the worksheet to have eight money columns, namely a debit and a credit column for each of four groups of gures: trial balance, adjustments, income statement, and balance sheet. The steps in completing the worksheet are, then, sim ilar to those for a service business (refer to 8 to review the steps).

If vce 0 (short-circuited) in the network of Fig. 6-1(b), then vcb vbe , so that, by KVL around the E; B loop, vbe hib ie hrb vcb hib ie hrb vbe h 1 ie rb vbe hib 1 hfb 1 hrb hob vbe hib

11 = 6

ib 1 hfb ie hob vcb Now, (1) and the given approximations, hie By (1.17), hre If ib 0, then ic ie in Fig. 6-1(b). By KVL,

KCL at node C then gives ic ie hfb ie hob vcb h ie ob 1 hfb hib hob v vbe 1 hfb ce

After rearranging, (3) and the given approximations lead to hre By (1.18), hfe ic ib vce 0 6 hrb 1 hfb hib hob h h % ib ob hrb hib hob hrb 1 1 hfb 1 hfb

Strategy: In calculating the volume of a solid of revolution we usually apply either the disk formula (or the washer formula) or the cylindrical shells formula (or the difference of cylindrical shells formula). To decide which formula to use: (1) Decide along which axis you are going to integrate. This depends on the shape and position of the region R that is revolved. (2) (i) Use the disk formula (or the washer formula) if the region R is revolved perpendicular to the axis of intergration. (ii) Use the cylindrical shells formula (or the difference of cylindrical shells formula) if the region R is revolved parallel to the axis of integration.

By KCL at node B of Fig. 6-1(b), with vce 0 (and thus vcb veb vbe , ib 1 hfb ie hob vcb 1 hfb ie hob vbe Solving (2) for vbe with ie ib ic and substituting now give ib 1 hfb ib ic hib hob i ic 1 hrb b