To solve this series-parallel circuit, we can break it down into smaller, easier-to-analyze parts. Let's start by identifying the resistors and their configurations.
In this circuit, we have five resistors: R1 = 10 ohms (first branch up), R2 = 10 ohms (second branch down), R3 = 20 ohms (second branch up), R4 = 25 ohms (first branch down), and R5 = 50 ohms (connecting both branches).
1. **Current (I)**: To find the current flowing through each resistor, we need to calculate the total current (I_total) first. Based on Ohm's Law, I = V / R, where V is the voltage and R is the resistance.
Given that we have a 12-volt battery, we can calculate the total current by summing up the individual currents in each branch. Each branch can be analyzed separately as series circuits, and then combine them as a parallel circuit.
First, let's calculate the current in the first branch (R1 and R4):
- Branch 1:
- Voltage drop (V1) = 12 volts
- Resistance (R1 + R4) = 10 + 25 = 35 ohms
- Current in branch 1 (I1) = V1 / (R1 + R4) = 12 V / 35 Ω
Now, let's calculate the current in the second branch (R2, R3, and R5):
- Branch 2:
- Voltage drop (V2) = 12 volts
- Resistance (R2 + R3 + R5) = 10 + 20 + 50 = 80 ohms
- Current in branch 2 (I2) = V2 / (R2 + R3 + R5) = 12 V / 80 Ω
Finally, summing up the individual currents, we get the total current (I_total) = I1 + I2.
2. **Voltage (V)**: The voltage across each resistor can be found using Ohm's Law (V = I * R), where I is the current flowing through the resistor and R is its resistance.
For the first branch:
- Voltage across R1 = I1 * R1
- Voltage across R4 = I1 * R4
For the second branch:
- Voltage across R2 = I2 * R2
- Voltage across R3 = I2 * R3
- Voltage across R5 = I2 * R5
3. **Power (P)**: The power consumed by each resistor can be calculated using the formula P = I * V.
For the first branch:
- Power consumed by R1 = I1 * V1 (or I1^2 * R1)
- Power consumed by R4 = I1 * V4 (or I1^2 * R4)
For the second branch:
- Power consumed by R2 = I2 * V2 (or I2^2 * R2)
- Power consumed by R3 = I2 * V3 (or I2^2 * R3)
- Power consumed by R5 = I2 * V5 (or I2^2 * R5)
By following these steps, you can find the current, voltage, and power for each resistor in the series-parallel circuit you described.