Three Resistors R1 = 80.9 Ω, R2 = 20.6 Ω, R3 = 70.0 Ω, And Two Batteries Emf1 = 40.0 V, And Emf2 = 359 V Are Connected In A Circuit With Three Branches. (a) What Current Flows Through R1, R2, And R3? (b) What Is The Absolute Value Of The Potential

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Introduction

In this article, we will explore a circuit consisting of three resistors and two batteries. The resistors have values of R1 = 80.9 Ω, R2 = 20.6 Ω, and R3 = 70.0 Ω, while the batteries have emf values of emf1 = 40.0 V and emf2 = 359 V. We will calculate the current flowing through each resistor and the absolute value of the potential difference across each resistor.

Circuit Diagram

Before we begin, let's visualize the circuit diagram. We have two batteries connected in series, with the positive terminal of the first battery connected to the negative terminal of the second battery. The three resistors are connected in parallel across the two batteries.

  +---------------+
  |  emf1 (40.0 V)  |
  +---------------+
           |
           |
           v
  +---------------+---------------+
  |  R1 (80.9 Ω)  |  R2 (20.6 Ω)  |
  +---------------+---------------+
           |           |
           |           |
           v           v
  +---------------+---------------+
  |  R3 (70.0 Ω)  |  emf2 (359 V)  |
  +---------------+---------------+

Calculating Current

To calculate the current flowing through each resistor, we need to find the equivalent resistance of the circuit. Since the resistors are connected in parallel, we can use the formula for parallel resistances:

1/R_total = 1/R1 + 1/R2 + 1/R3

We can plug in the values of the resistors and calculate the equivalent resistance:

1/R_total = 1/80.9 + 1/20.6 + 1/70.0 R_total = 14.1 Ω

Now that we have the equivalent resistance, we can calculate the current flowing through each resistor using Ohm's law:

I = V/R

We can plug in the values of the voltage and resistance for each resistor:

I1 = 40.0/80.9 = 0.495 A I2 = 40.0/20.6 = 1.94 A I3 = 359/70.0 = 5.13 A

Calculating Potential Difference

To calculate the absolute value of the potential difference across each resistor, we can use Ohm's law:

V = IR

We can plug in the values of the current and resistance for each resistor:

V1 = 0.495 x 80.9 = 40.0 V V2 = 1.94 x 20.6 = 40.0 V V3 = 5.13 x 70.0 = 359 V

Conclusion

In this article, we calculated the current flowing through each resistor and the absolute value of the potential difference across each resistor in a circuit consisting of three resistors and two batteries. We found that the current flowing through R1, R2, and R3 are 0.495 A, 1.94 A, and 5.13 A, respectively. The absolute value of the potential difference across R1, R2, and R3 are 40.0 V, 40.0 V, and 359 V, respectively.

References

Future Work

In the future, we can explore more complex circuits and calculate the current and potential difference across each component. We can also investigate the effects of different resistor values and battery emf on the circuit.

Code

The code used to calculate the current and potential difference is as follows:

import math

R1 = 80.9
R2 = 20.6
R3 = 70.0
emf1 = 40.0
emf2 = 359



R_total = 1 / (1/R1 + 1/R2 + 1/R3)



I1 = emf1 / R1
I2 = emf1 / R2
I3 = emf2 / R3



V1 = I1 * R1
V2 = I2 * R2
V3 = I3 * R3


print("Current flowing through R1:", I1)
print("Current flowing through R2:", I2)
print("Current flowing through R3:", I3)
print("Absolute value of potential difference across R1:", V1)
print("Absolute value of potential difference across R2:", V2)
print("Absolute value of potential difference across R3:", V3)


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