please show all work ! thanks Find the potential difference across each resistor

Question

please show all work ! thanks

Find the potential difference across each resistor in the figure below. (R1 = 5.40 ?, R2 = 4.20 ?, R3 = 2.80 ?, R4 = 1.80 ?)

?V1 =  
Apply Kirchhoff's rules to write a set of simultaneous equations that can be solved for the current through the resistor R1 and then use your results to find the potential difference requested. V ?V2 =  V ?V3 =  V ?V4 =  V please show all work ! thanks Find the potential difference across each resistor in the figure below. (R1 = 5.40 ?, R2 = 4.20 ?, R3 = 2.80 ?, R4 = 1.80 ?) Apply Kirchhoff's rules to write a set of simultaneous equations that can be solved for the current through the resistor R1 and then use your results to find the potential difference requested. V

Explanation / Answer

Let there be two loops with currents I1 andI2, both in clock wise direction.

loop 1

5.40 I1 - 12 + 3 + 4.20 (I1 - I2) = 0

=> 9.60 I1 -4.20 I2 = 9                 (1)

loop 2

1.80 I2 + 2.80 I2 + 4.20 (I2 - I1 ) -3 + 18 = 0

=> -4.20 I1 + 8.8 I2 = -15                 (2)

Solving 1 and 2 we get

I1 =       0.24237 A         I2 = -1.58886 A

Now V1 = 0.24237 * 5.40 = 1.3088 V (ans)

V2 = 4.20 ( 0.24237 + 1.58886 ) = 7.69 V (ans)

V3 = 2.80 * 1.58886 = 4.4488 V (ans)

V4 = 1.80 * 1.58886 = 2.86 V (ans)

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