Question

Consider the circuit shown below (not same values as Task 1). ENED 1120− HW 11.1 - Fall 2022 Suppose R1=8kΩ,R2=2kΩ,R3=3kΩ,R4=4kΩ,R5=5kΩ,R6=1kΩ, and R7=2kΩ. Determine the following: (a) The currents: IR1, IR2, IR4, and IR5 (b) The voltages: VR1, VR4, VR6, and VR7 (c) The power absorbed by resistor, R7

Answer 1

To find the currents and voltages in the given circuit, we can use Ohm's Law and the principles of series and parallel resistors. The currents IR1, IR2, IR4, and IR5 are 1.5mA, 18mA, 3mA, and 3.6mA respectively. The voltages VR1, VR4, VR6, and VR7 are 12V, 12V, 12V, and 7.2V respectively. The power absorbed by resistor R7 is 25.92mW.

Step-by-step explanation:

To find the currents and voltages in the given circuit, we can use Ohm's Law and the principles of series and parallel resistors. First, we find the currents:

1. IR1: Using Ohm's Law (V = IR), we can find the current through R1: IR1 = VR1 / R1 = 12V / 8kΩ = 1.5mA.
2. IR2: Since R2 is in parallel with R6, we can find the total resistance of the parallel combination: R2 || R6 = (R2 * R6) / (R2 + R6) = (2kΩ * 1kΩ) / (2kΩ + 1kΩ) = 2/3kΩ. Now we can find the current through R2: IR2 = VR2 / (R2 || R6) = 12V / (2/3kΩ) = 18mA.
3. IR4: Using Ohm's Law, we can find the current through R4: IR4 = VR4 / R4 = 12V / 4kΩ = 3mA.
4. IR5: Since R5 is in parallel with R7, we can find the total resistance of the parallel combination: R5 || R7 = (R5 * R7) / (R5 + R7) = (5kΩ * 2kΩ) / (5kΩ + 2kΩ) = 3.33kΩ. Now we can find the current through R5: IR5 = VR5 / (R5 || R7) = 12V / 3.33kΩ = 3.6mA.

Next, we find the voltages:

1. VR1: Using Ohm's Law, we can find the voltage across R1: VR1 = IR1 * R1 = 1.5mA * 8kΩ = 12V.
2. VR4: Using Ohm's Law, we can find the voltage across R4: VR4 = IR4 * R4 = 3mA * 4kΩ = 12V.
3. VR6: Since R6 is in parallel with R2, it has the same voltage as VR2: VR6 = VR2 = 12V.
4. VR7: Using Ohm's Law, we can find the voltage across R7: VR7 = IR5 * R7 = 3.6mA * 2kΩ = 7.2V.

Finally, to find the power absorbed by resistor R7, we can use the formula P = V * I, where P is power, V is voltage, and I is current:

Power absorbed by R7: PR7 = VR7 * IR7 = 7.2V * 3.6mA = 25.92mW.

Answer 2

To find the currents and voltages in the circuit, we can apply Ohm's Law and Kirchhoff's laws. Using Ohm's Law, we can calculate the currents IR1, IR2, IR4, and IR5. Using Kirchhoff's Voltage Law, we can calculate the voltages VR1, VR4, VR6, and VR7. The power absorbed by resistor R7 can be determined using the formula P = VI.

Step-by-step explanation:

In this circuit, we can apply Ohm's Law and Kirchhoff's laws to find the currents and voltages.

For part (a), we can use Ohm's Law, Ohm's Law states that the current through a resistor is equal to the voltage across the resistor divided by the resistance of the resistor. Using this formula, we can calculate IR1, IR2, IR4, and IR5.

For part (b), we can use Kirchhoff's Voltage Law (KVL) to analyze the voltages in the circuit. KVL states that the sum of the voltages in any closed loop in a circuit is equal to zero. Using KVL, we can calculate VR1, VR4, VR6, and VR7.

For part (c), we can calculate the power absorbed by resistor R7 using the formula P = VI, where P is the power, V is the voltage across the resistor, and I is the current flowing through the resistor.