Please help! Somewhere I got my loop rules wrong and messed it all up Find the p

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Please help! Somewhere I got my loop rules wrong and messed it all up

Find the potential difference across each resistor in the figure below. (R_1 = 4.80 ohm, R_2 = 3.80 ohm, R_3 = 2.80 ohm, R_4 = 1.80 ohm) delta V_1 Apply Kirchhoff's rules to write a set of simultaneous equations that can be solved for the current through the resistor R_1 and then use your results to find the potential difference requested. V delta V_2 Apply Kirchhoff's rules to write a set of simultaneous equations that can be solved for the current through the resistor R_2 and then use your results to find the potential difference requested. V delta V_3 Apply Kirchhoff's rules to write a set of simultaneous equations that can be solved for the current through the resistor R_3 and then use your results to find the potential difference requested. V delta V_4 Apply Kirchhoff's rules to write a set of simultaneous equations that can be solved for the current through the resistor R_4 and then use your results to find the potential difference requested. V

Explanation / Answer

let I1,I2 and I3 are the currents through R1,R2 and R3 respectively.

Apply KVL in left loop,

12 - 3 - 3.8*I2 - 4.8*I1 = 0 -------(1)

Apply KVL in right loop

18 - 3 - 3.8*I2 - I3*(2.8 + 1.8) = 0 -----(2)

At the junction,

I1 + I3 = I2   ----(3)

on solving the above three equations we get

I1 = 0.322 A
I2 = 1.962 A
I3 = 1.64 A

so,

delta_V1 = I1*R1 = 0.322*4.8 = 1.54 V

delta_V2 = I2*R2 = 1.962*3.8 = 7.46 V

delta_V3 = I3*R3 = 1.64*2.8 = 4.59 V

delta_V4 = I3*R4 = 1.64*1.8 = 2.95 V

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