How to solve circuit theory using mesh analysis
1 answer:
Explanation:
Find a minimal set of cycles that covers all vertices and edges of the circuit graph. For each cycle, define a "mesh" current, and write the Kirchhoff's Voltage Law (KVL) equation with respect to each of the edges in the cycle. Where an edge is part of more than one cycle, all current(s) defined for the edge will contribute to the voltage there.
This will give as many equations as there are mesh currents. Solve the resulting system of equations. The (signed) sum of the mesh currents through any edge is the current in that circuit branch.
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<u>Example</u>
Consider the attached circuit. It shows mesh currents I1, I2, and I3 in graph cycles with those numbers. The KVL equations are ...
mesh 1: I1(R3 +R2 +R1) -I2·R1 -I3·R2 = Vi (the voltage across the current source)
mesh 2: -I1·R1 +I2(r1 +1/(sC)) -I3(1/(sC)) = Vs
mesh 3: -I1·R2 -I2(1/(sC)) +I3(R2 +sL +1/(sC)) = 0
You will note that the matrix of equation coefficients is symmetric.
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In this example, you will end with I1 as a function of Vi. If I1 is a given source value, that relation can be used to find Vi.
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Answer:
the endurance strength = 421.24 MPa
Explanation:
From the given information; The objective is to estimate the endurance strength, Se, in MPa .
To do that; let's for see the expression that shows the relationship between the ultimate tensile strength and Brinell hardness number .
It is expressed as:
where;
= Brinell hardness number
= Ultimate tensile strength
From ;
; replace 290 for
; we have
988.9 MPa
We can see that the derived value for the ultimate tensile strength when the Brinell harness number = 290 is less than 1400 MPa ( i.e it is 988.9 MPa)
So; we can say
The Endurance limit can be represented by the formula:
= 494.45 MPa
Using Table 6.2 for parameter for Marin Surface modification factor. The value for a and b are derived; which are :
a = 1.58
b = -0.085
The value of the surface factor can be calculate by using the equation
The formula that is used to determine the value of for the rotating shaft of size factor d = 10 mm is as follows:
Finally; the the endurance strength, Se, in MPa if the rod is used in rotating bending is determined by using the expression;
= 0.8792×0.969×494.45
= 421.24 MPa
Thus; the endurance strength = 421.24 MPa