Final answer:
The Varley loop test is related to locating faults in underground cables but the information provided is insufficient to answer the student's question. Instead, detailed methods are explained for calculating the resistance of a coaxial cable and determining total resistance for series and parallel resistor circuits, which are standard physics calculations.
Step-by-step explanation:
The Varley Loop Test is a method used to locate faults in underground cables. In the context provided by the student, the Varley loop test involves a circuit with known fixed resistances P and Q, and variable resistances S1 and S2 at different positions. Unfortunately, the provided information does not describe the full setup of a Varley loop test, such as the balance conditions or the methods used to determine the fault distance, so it is not possible to use this information directly to calculate the length of cable or distance to the fault. Instead, we will address two provided problems that are unrelated to the Varley loop test but are firmly within the subject of physics:
- Coaxial cable resistance: To find the resistance of a coaxial cable with inner radius ri, outer radius ro, length L, and resistivity ρ of the insulating material, use the formula R = (ρ∙ln(ro/ri))/(2π∙L). For plastic with a resistivity of 2.00 × 10¹³ Ω∙m, inner radius 0.25 cm, outer radius 0.5 cm, and length 10 meters, the resistance R can be calculated.
- Series and parallel resistor circuits: For resistors in parallel, the total resistance can be found with 1/R_total = 1/R1 + 1/R2. For resistors in series, the total resistance is simply R_total = R1 + R2. To calculate the total resistance for a given series or parallel circuit, substitute the known resistance values into these formulas accordingly.
The information about the coaxial cable and resistors in series and parallel circuits is useful for solving a variety of electrical engineering problems in physics.