a. Explanation Given data: Refer the given reference problem in the question. Formula used: Write the expression to calculate the percent error. % error = [ approximate value true value − 1 ] × 100 (1) Calculation: Modify the given figure with the representation of node voltages as shown in Figure 1. From Figure 1, write the expression for voltage v a using voltage division rule. v a = v i n R 4 R 4 + R o + Δ R (2) From Figure 1, write the expression for voltage v b using voltage division rule. v b = v i n R 3 R 2 + R 3 (3) Write the expression for output voltage v o . v o = v a − v b (4) Substitute the equations (2) and (3) in (4). v o = v i n R 4 R 4 + R o + Δ R − v i n R 3 R 2 + R 3 (5) When the bridge is in balanced condition, the value of Δ R and v o is equal to zero. v i n R 4 R 4 + R o = v i n R 3 R 2 + R 3 R 4 R 4 + R o = R 3 R 2 + R 3 (6) Substitute equation (6) in (5). v o = v i n R 4 R 4 + R o + Δ R − v i n R 4 R 4 + R o = v i n R 4 [ 1 R 4 + R o + Δ R − 1 R 4 + R o ] v o ( true ) = v i n R 4 [ − Δ R ( R 4 + R o + Δ R ) ( R 4 + R o ) ] (7) The above expression is the true value of output voltage. Since Δ R ≪ R 4 , the approximate value of v o is given below. v o ≈ v i n R 4 [ − Δ R ( R 4 + R o ) ( R 4 + R o ) ] v o ( approx ) = ( − Δ R ) R 4 v i n ( R 4 + R o ) 2 (8) Since both true and approximate values of output voltage are negative, modify equation (1) as given below. % error = [ true value approximate value − 1 ] × 100 (9) Substitute the equations (7) and (8) in (9) b. To determine Calculate the percentage error in v o .

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Chapter 3, Problem 70P

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Show that the percent error in the approximation of vo is % error=−(ΔR)R3(R2+R3)R4×100.

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Calculate the percentage error in vo.

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Chapter 3, Problem 69P

Chapter 3, Problem 71P

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