For the circuit shown below with a 12.0 V battery, find the total current through the battery and the current through each resistor with the following resistances: R1=5.0 Ohms, R2=10.0 Ohms, R3=15.0 Ohms, R4=33.0 Ohms. Show all your work!

The total current through the battery is 4.77 A.
The current through resistor R1 is 2.4 A.
The current through resistor R2 is 1.2 A
The current through resistor R3 is 0.8 A
The current through resistor R4 is 0.36 A.
The total resistance of the circuit is calculated as follows;
1/Rt = 1/Rā + 1/Rā + 1/Rā + 1/Rā
1/Rt = 1/5 + 1/10 + 1/15 + 1/33
1/Rt = 0.397
Rt = 1/0.397
Rt = 2.518 ohms
I = V/Rt
I = 12/2.518
I = 4.77 A
Iā = V/Rā
Iā = 12/5
Iā = 2.4 A
Iā = 12/10
Iā = 1.2 A
Iā = 12/15
Iā = 0.8 A
Iā = 12/33
Iā = 0.36 A
Thus, the total current through the battery is 4.77 A.
The current through resistor R1 is 2.4 A.
The current through resistor R2 is 1.2 A
The current through resistor R3 is 0.8 A
The current through resistor R4 is 0.36 A.
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