JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech I Year BASIC ELECTRICAL AND ELECTRONICS ENGINEERING Previous Question Paper (September/October - 2021 - R16)

To reduce a circuit to a simple equivalent resistance, we apply the principles of series and parallel combinations:

• Identify resistors connected in series, where the current remains the same. The equivalent resistance is the sum of individual resistances: R_eq = R₁ + R₂ + ... + R_n.
• Identify resistors connected in parallel, where the voltage across them is the same. The equivalent resistance is calculated using the reciprocal formula: 1/R_eq = 1/R₁ + 1/R₂ + ... + 1/R_n.
• For two parallel resistors, use the simplified product-over-sum formula: R_eq = (R₁ * R₂) / (R₁ + R₂).
• Systematically simplify the circuit starting from the branch furthest from the terminals, replacing series or parallel groups with their equivalent values until only one resistor remains.

To determine the equivalent resistance R_XY across terminals X and Y, follow these systematic steps:

• Step 1: Simplify internal loops. Identify any resistors that are strictly in series or parallel within the network. Replace them with their equivalent values.
• Step 2: Apply Delta-to-Wye (Δ-Y) or Wye-to-Delta (Y-Δ) transformations. If the circuit contains bridge configurations or nodes that are neither purely series nor parallel, use the transformation formulas to simplify the topology. For a Delta network with resistances R_a, R_b, R_c, the equivalent Wye resistances are R₁ = (R_bR_c)/(R_a+R_b+R_c), R₂ = (R_aR_c)/(R_a+R_b+R_c), and R₃ = (R_aR_b)/(R_a+R_b+R_c).
• Step 3: Redraw and reduce. After transformation, the circuit will typically simplify into a series-parallel network. Continue combining resistors until a single equivalent resistance remains between terminals X and Y.
• Step 4: Verification. Ensure that no short circuits or open circuits are ignored during the reduction process.