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2010Midterm1

# 2010Midterm1 - Power = V TH R L R TH ± 2 R TH = 18.75 W A...

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a) How many nodes, branches, and independent loops are there in the circuit respectively? Figure 1 According to Figure 1, there are 3 nodes, 6 branches, and 4 independent loops. b) When R L = 6Ω, find current I x . Figure 2 In Figure 2, apply nodal analysis: Node 1: V 1 = 32 V Node 2: V1 V2 4 + 2 = V2 0 12 + V2 0 6 + V2 0 1 Results: V 2 = 20/3 V, I x = V2/12=5/9 A c) Find the Thevenin equivalent circuit between the terminals a and b. Figure 3 In Figure 3, V TH = V ab . Apply nodal Analysis: Node 1: V 1 = 32V Node 2: V1 V2 4 + 2 = V2 0 12 + V2 0 1
Results: V 2 = V ab = V TH = 7.5 V Figure 3 In Figure 4, Calculate R TH : R TH = 4 Ω || 12 Ω || 1 Ω = 1/( 1/4+1/12+1/1 ) Ω = 0.75 Ω Thevenin equivalent circuit is as in Figure 4. Figure 4 d) Find the value of R L when the power delivered to R L becomes maximum. What is the maximum power through R L ? When the power of R L is maximum. R L = R TH = 0.75 Ω .

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Unformatted text preview: Power = V TH R L +R TH ± 2 R TH = 18.75 W A Wheatstone bridge, shown on the right, is used to measure the resistance across R x . It is considered balanced when the voltage V G is zero. R 2 is an adjustable resistor. R 1 = 200 Ω, and R 3 = 400 Ω. 1. Derive an equation for R x in terms of R 1 , R 2 , and R 3 when the circuit is balanced. Applying voltage division principle v R R R V v R R R V x x Rx R 3 2 1 2 2 x x R R R R R R 3 2 1 2 x R R R R 1 3 2 1 3 2 R R R R x 2. If R x has an expected range of 500 Ω to 2 kΩ, what range will be required of R 2 to balance the circuit? 3 1 2 R R R R x 250 400 200 * 500 ) low ( 2 R 1000 400 200 * 000 , 2 ) high ( 2 R R 2 has a range of 250 Ω to 1 kΩ...
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2010Midterm1 - Power = V TH R L R TH ± 2 R TH = 18.75 W A...

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