Series and Parallel Circuit PDF

# Series and Parallel Circuit ## Series: - Diagram: A circuit with three resistors in a row, labeled R1, R2, and R3. The ends of the resistors are connected together, and the current flows through all three resistors. - Formula: R = R1 + R2 + R3 - Description: - The current is the same acro...

# Series and Parallel Circuit ## Series: - Diagram: A circuit with three resistors in a row, labeled R1, R2, and R3. The ends of the resistors are connected together, and the current flows through all three resistors. - Formula: R = R1 + R2 + R3 - Description: - The current is the same across the resistors. - The voltage in each resistor is different and given by using the voltage division law \[VDL\] - Using V = IR and the formula for R (R = R1 + R2 + R3), you can get that V1 = V(R1 / (R1 + R2 + R3)) and V2 = V(R2 / (R1 + R2 + R3)). ## Parallel: - Diagram: A circuit with three resistors connected in parallel. The first two resistors are in a rectangle, with the third resistor at the end. The current flows through all three resistors. - Formula: 1/R = 1/R1 + 1/R2 + 1/R3 - Description: - The voltage is the same across all the resistors. - The current is different for each resistor. - This can be calculated using the *current division law (CDL)* - The formula can be rewritten as R = (R1 * R2 * R3) / (R1 * R2 + R1 * R3 + R2 * R3) ## Exercises: **1.** Determine the total resistance between the terminals A and B - Diagram: A circuit with different resistors arranged in series and parallel branches. Resistors are connected in parallel across points A and B. - Solution: - The resistors in the branch above point A are connected in series (1Ω + 2Ω = 3Ω). - Resistors inside the branch are also connected in series (1Ω + 2Ω = 3Ω). - In parallel: 1/R = 1/R1 + 1/R2 - 1/R = 1/3 + 1/3 - 1/R = 2/3 - R = 3/2 = 1.5 - All three resistors are connected in series ( 1.5Ω + 4Ω + 3Ω = 8.5Ω) - Total resistance = **8.5Ω** **2.** Determine the total resistance between the terminals A and B - Diagram: Two parallel branches of series resistors. - Branch 1 has resistors with values of 8Ω, 3Ω, and 8Ω, and a total resistance of 19Ω. - Branch 2 has resistors with values of 8Ω, 3Ω, and 8Ω, and a total resistance of 19Ω. - Solution: - Branch 1 is in series (8Ω + 3Ω + 8Ω = 19Ω) - Branch 2 is in series (8Ω + 3Ω + 8Ω = 19Ω) - Two branches are in parallel: 1/R = 1/R1 + 1/R2 - 1/R = 1/19 + 1/19 - 1/R = 2/19 - R = 19 / 2 = 9.5 - Total resistance = **9.5Ω** **3.** Two resistors 3 Ω and 6 Ω are connected in 10V. Determine: - a) the current (total) and current in each resistor - b) the voltage in each resistor - c) the power in each resistor and the total power - d) the total energy consumed in 50 minutes. **4.** How much is the voltage drop across each resistance? - Diagram: A circuit with three resistors in series, each with 50kΩ resistance. - Solution: - The voltage is the same across the resistors. - The current is different for each resistor. - The total resistance is 50kΩ + 50kΩ + 50kΩ = 150kΩ. - The current in each resistor is equal to 180V / 150kΩ = 1.2 mA. - The voltage drop across each resistor is equal to the current * the resistance = 1.2 mA * 50kΩ = 60V. - The total voltage drop across all three resistors is 60V + 60V + 60V = 180V.