Question:
Find current and voltage across resistors R1 and R2, when they connected in parallel and in series. A 12V battery is connected, R1=4Ω and R2=3Ω.
Methods:
First of all, we try to find a circuit where resistors are connected in parallel. When resistors are connected in parallel, the voltage across each resistor is exactly the same, V1 = V2 = 12 V. On the other hand, parallel circuits are currents dividers. To find current across each resistor we use Ohm’s law I=V/R, then I1=V1/R1=12/4=3A and I2=V2/R2=12/3=4A. Total current (not asked) in a circuit would be I1+I2=7A. To check if our total current is right, we can find total resistance and use Ohm’s law on the whole circuit. The total resistance in a parallel circuit is found using formula 1/Rt=1/R1+1/R2, which is equal to Rt=R1R2/(R1+R2)= 34/(3+4)=12/7≈1.714Ω. Then total current I=V/Rt=12/(12/7)=7A. Correct!2)When resistors are connected in series, the current is the same in every resistor and is equal to that coming from the battery. To find this current we need to use Ohm’s law. The total resistance in series combination is just a sum of both resistors Rt=R1+R2=3+4=7Ω. I=V/Rt=12/7A≈1.714A. To find the voltage across each resistor we can use Ohm’s law again and V1=IR1=12/74=48/7V≈6.86V; V2=IR2=12/73=36/7V≈5.14V.
To check if our result is right we can sum both voltages V1+V2=48/7+36/7=12V.
Correct!
Answer:
First of all, we try to find a circuit where resistors are connected in parallel. When resistors are connected in parallel, the voltage across each resistor is exactly the same, V1 = V2 = 12 V. On the other hand, parallel circuits are currents dividers. To find current across each resistor we use Ohm’s law I=V/R, then I1=V1/R1=12/4=3A and I2=V2/R2=12/3=4A. Total current (not asked) in a circuit would be I1+I2=7A. To check if our total current is right, we can find total resistance and use Ohm’s law on the whole circuit. The total resistance in a parallel circuit is found using formula 1/Rt=1/R1+1/R2, which is equal to Rt=R1R2/(R1+R2)= 34/(3+4)=12/7≈1.714Ω. Then total current I=V/Rt=12/(12/7)=7A. Correct!2)When resistors are connected in series, the current is the same in every resistor and is equal to that coming from the battery. To find this current we need to use Ohm’s law. The total resistance in series combination is just a sum of both resistors Rt=R1+R2=3+4=7Ω. I=V/Rt=12/7A≈1.714A. To find the voltage across each resistor we can use Ohm’s law again and V1=IR1=12/74=48/7V≈6.86V; V2=IR2=12/73=36/7V≈5.14V. To check if our result is right we can sum both voltages V1+V2=48/7+36/7=12V. Correct!
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