can scan your paper and upload a digital copy to Canvas OR you can turn in a har

Question

can scan your paper and upload a digital copy to Canvas OR you can turn in a hard copy of the problems n class Part 1: Analyze the following circuit 3 2 1 13A 1 3 1 How many unknowns are there in this system? Create a vector x containing the unknowns, which could be current, resistance, or voltage values. Use Ohm's Law and Kirchoff's Voltage and Current Laws to write down the necessary number of equations to solve for these unknown. 2. . Solve the equations by hand to find the values of the unknowns. 4. Create a matrix equation of the form Ax = b using the vector x from Problem 1.

Explanation / Answer

1 )

three are unknown in the given system

I1 following a to b is x1 and

I2 following c to b is x2 and

Voltage supplies the current d to c is x3

so x have unknowns is x [ 3:1 ]

b )

using KVL

60 - 3 I1 + 80 - I1 = 0 ------------1

and E - 2 I2 + 80 - 3 I2 = 0 ---------- 2

and I1 + I2 + I3 = 0 ----------- 3

3 )

from 1 we get I1 =35 A

from 2 and 3

we get I2 = - 48 A

I2 value in equation 2

we get E = - 320 volts

4 )

I1 = 140 A and x1 = 140 ---------- i

from eq

3 x1 + x2 = - 13 -------- ii

from eq 2

E - 2 I2 + 80 - 3 I2 = 0

- 5 x2 + x3 = 80 --------- iii

now solving equation i , ii and iii as

Ax = b

| 1   0    0 |

A =   | 1   1 0 |

        | 0   -5   1 |

and

        | x1 |

x =   | x2 |

      | x3 |

and

        | 140 |

B =   | - 13 |

      | - 80 |

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