Question:
Q.3. (a) Find the equivalent resistance (all resistors R = 50Ω).
(b) Calculate the power delivered to the last resistor (on the right) if a 20 Volt battery is attached between points A and B.
Q.3. (a) Find the equivalent resistance (all resistors R = 50Ω).
(b) Calculate the power delivered to the last resistor (on the right) if a 20 Volt battery is attached between points A and B.
Answer:
Step 1: Understand the circuit configuration
Given that all resistors have a value of R = 50Ω, the combination involves both series and parallel connections.
Given that all resistors have a value of R = 50Ω, the combination involves both series and parallel connections.
Step 2: Calculate equivalent resistance
R₁₂ = (R × 2R) / (R + 2R) = 2R / 3
R₁₂₃ = 2R/3 + R = 5R / 3
R₁₂₃₄ = (5R/3 × 2R) / (5R/3 + 2R) = 10R / 11
R_AB = 10R / 11 + R = 21R / 11 = (21 × 50) / 11 = 95.46 Ω
Step 3: Current in the circuit
Using Ohm’s Law:
Using Ohm’s Law:
I = V / R_AB = 20 / 95.46 ≈ 0.21 A
Step 4: Current through each branch
Current through resistor 3:
Current through resistor 3:
i₃ = 2i × 3 / 11 = 2 × 0.21 × 3 / 11 = 0.12 A
Current through resistor 1:
i₁ = i₃ × (2 / 3) = 0.12 × 2 / 3 = 0.08 A
Step 5: Power delivered to last resistor
Using the power formula:
Using the power formula:
P = i² × R = (0.08)² × 50 = 0.32 W
Final Answers:
(a) Equivalent Resistance = 95.46 Ω
(b) Power Delivered to Last Resistor = 0.32 W
(a) Equivalent Resistance = 95.46 Ω
(b) Power Delivered to Last Resistor = 0.32 W