Consider the following figure. Note: The currents are not necessarily in the dir

Question

Consider the following figure. Note: The currents are not necessarily in the direction shown. (Assume R_1 = 26.0 Ohm, R_2 = 5.0 Ohm, and V = 33 V.) (a) Find the current in each resistor of the figure above by using the rules for resistors in series and parallel. 5.0 Ohm A 26.0 Ohm A 24 Ohm A (b) Write three independent equations for the three currents using Kirchoff's laws: one with the node rule; a second using the loop rule through the battery, the 5.0- Ohm resistor, and the 24.0- Ohm resistor; and the third using the loop rule through the 26.0- Ohm and 24.0- Ohm resistors. Solve to check the answers found in part (a). (Submit a file with a maximum size of 1 MB.)

Explanation / Answer

R1 and 24 ohm are in parallel and their combination is given as

Rs = R1 24 /(R1 + 24) = 26 x 24 /(26 + 24) = 12.48 ohm

Rs and R2 are in series and their combination is given as

Rtotal = Rs + R2 = 12.48 + 5 = 17.48 ohm

since R2 is in series with the battery

hence Itotal = I2 = V/Rtotal = 33/17.48 = 1.89 A

V2 = I2 R2 = 1.89 x 5 = 9.5 volts

V1 = V - V2 = 33 - 9.5 = 23.5 volts

I1 R1 = V1

I1 (26) = 23.5

I1 = 0.904 A

I24 = I2 - I1 = 1.89 - 0.904 = 0.986 A

b)

using KCL

I2 = I1 + I24

I24 = I2 - I1    eq-1

using KVL

I2 R2 + I1 R1 = V

5 I2 + 26 I1 = 33

I1 = (33 - 5 I2 )/26                     eq-2

using KVL

I2 R2 + I24 (24) = V

5 I2 + (I2 - I1 )(24) = 33

using eq-2

5 I2 + (I2 - ((33 - 5 I2 )/26))(24) = 33

I2 = 1.89 A

using eq-2

I1 = (33 - 5 I2 )/26 = (33 - 5 (1.89) )/26 = 0.904 A

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