Find the potential difference across each resistor in the figure below. (R1 = 5.24 , R2 = 3.85 , R3 = 3.30 , R4 = 2.00 )
VR1 = V
VR2 = V
VR3 = V
VR4 = V
|----|------|
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___ ___ ___
12V 3V 18V
- - -
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R1 R2 R4
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|_____|_R3__|
I have no idea what your circuit looks like.
To find the potential difference (V) across each resistor, you need to apply Ohm's law, which states that the potential difference across a resistor is equal to the current (I) flowing through it multiplied by its resistance (R).
However, in order to use Ohm's law, we need to determine the current flowing through each resistor. To find the current, we can use the concept of series and parallel resistors.
From the given circuit, we can see that R1 and R2 are in series, and their combined resistance (RT1-2) is equal to the sum of their resistances:
RT1-2 = R1 + R2 = 5.24Ω + 3.85Ω = 9.09Ω
Similarly, R3 and R4 are also in series, and their combined resistance (RT3-4) is equal to the sum of their resistances:
RT3-4 = R3 + R4 = 3.30Ω + 2.00Ω = 5.30Ω
Now, the combination of RT1-2 and RT3-4 is in parallel. The total resistance in the parallel combination (RTotal) can be found using the formula:
1/RTotal = 1/RT1-2 + 1/RT3-4
1/RTotal = 1/9.09 + 1/5.30
1/RTotal = 0.110 + 0.189
1/RTotal = 0.299
RTotal = 1 / 0.299 = 3.35Ω
Next, to find the current flowing through the entire circuit (ITotal), you can use Ohm's law:
ITotal = VTotal / RTotal
Given that VTotal is 12V, we have:
ITotal = 12V / 3.35Ω = 3.58A
Now, we can find the current flowing through each resistor:
For resistors R1 and R2 (in series), the current flowing through them is the same:
IR1-2 = ITotal = 3.58A
For resistors R3 and R4 (in series), the current flowing through them is also the same:
IR3-4 = ITotal = 3.58A
Finally, we can calculate the potential difference (V) across each resistor using Ohm's law:
VR1 = IR1-2 * R1 = 3.58A * 5.24Ω = 18.76V
VR2 = IR1-2 * R2 = 3.58A * 3.85Ω = 13.79V
VR3 = IR3-4 * R3 = 3.58A * 3.30Ω = 11.81V
VR4 = IR3-4 * R4 = 3.58A * 2.00Ω = 7.16V
Hence, the potential differences across each resistor are:
VR1 = 18.76V
VR2 = 13.79V
VR3 = 11.81V
VR4 = 7.16V