The equivalent resistance between the terminal A and B?
Introduction:
In this question, we are given a circuit with resistors connected in a specific pattern and we need to find the equivalent resistance between the terminals A and B. To solve this problem, we will analyze the circuit using the principles of series and parallel resistors.
Analysis:
To simplify the circuit, we can start by identifying the different sections of the circuit and then find the equivalent resistance for each section. Finally, we can combine these equivalent resistances to find the overall equivalent resistance between terminals A and B.
Section 1:
In the first section of the circuit, resistors R1 and R2 are connected in series. The equivalent resistance for these two resistors in series can be calculated by simply adding their individual resistances:
R_eq1 = R1 + R2
Section 2:
In the second section of the circuit, resistors R3 and R4 are connected in parallel. The equivalent resistance for two resistors in parallel can be calculated using the formula:
1/R_eq2 = 1/R3 + 1/R4
Simplifying this equation, we get:
R_eq2 = (R3 * R4) / (R3 + R4)
Section 3:
In the third section of the circuit, resistor R5 is connected in series with the equivalent resistance of section 2 (R_eq2). The equivalent resistance for these two resistors in series can be calculated by adding their individual resistances:
R_eq3 = R5 + R_eq2
Section 4:
In the fourth section of the circuit, resistor R6 is connected in parallel with the equivalent resistance of section 3 (R_eq3). The equivalent resistance for two resistors in parallel can be calculated using the formula:
1/R_eq4 = 1/R6 + 1/R_eq3
Simplifying this equation, we get:
R_eq4 = (R6 * R_eq3) / (R6 + R_eq3)
Overall Equivalent Resistance:
Finally, in the last section of the circuit, the equivalent resistance of section 4 (R_eq4) is connected in series with resistor R7. The overall equivalent resistance between terminals A and B can be calculated by adding their individual resistances:
R_eq = R_eq4 + R7
Conclusion:
By analyzing the circuit and applying the principles of series and parallel resistors, we can find the equivalent resistance between terminals A and B. This approach allows us to break down the complex circuit into simpler sections and calculate their equivalent resistances. Finally, by combining these equivalent resistances, we can determine the overall equivalent resistance of the circuit.
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