A circuit is constructed with five resistors and a battery as shown. The battery voltage is V = 12 V. The values for the resistors are: R1 = 65 ?, R2 = 111 ?, R3 = 173 ?, and R4 = 96 ?. The value for RX is unknown, but it is known that I4, the current that flows through resistor R4, is zero.
1)What is I1, the magnitude of the current that flows through the resistor R1?
2)What is V2, the magnitude of the voltage across the resistor R2?
3)What is I2, the magnitude of the current that flows through the resistor R2?
4)What is RX, the value of the unknown resistor RX?
5)What is V1, the magnitude of the voltage across the resistor R1?
The correct answer and explanation is :
To solve this circuit problem, we analyze the configuration using principles of series and parallel circuits, along with Ohm’s Law. The key detail is that the current through resistor R4 is zero (I4 = 0), indicating no potential difference across R4. This implies that the voltage at both ends of R4 is the same, leading to the conclusion that the voltage drop across R1 equals the voltage drop across R2.
1) What is I1, the magnitude of the current that flows through resistor R1?
Given that the voltage across R1 is equal to the voltage across R2, and using Ohm’s Law (V = IR), we can write:
V1 = I1 × R1
V2 = I2 × R2
Since V1 = V2, we have:(Mohawk Valley Community College)
I1 × R1 = I2 × R2
This relation allows us to express I2 in terms of I1:(uodiyala.edu.iq)
I2 = (R1 / R2) × I1(uodiyala.edu.iq)
To find I1, we need to determine the total resistance in the circuit and use the total voltage to find the total current. However, due to the complexity of the circuit and the unknown resistor RX, we need more information or a circuit diagram to proceed with exact calculations.
2) What is V2, the magnitude of the voltage across resistor R2?
As established, V2 = V1. Without the value of I1, we cannot compute V2 directly.
3) What is I2, the magnitude of the current that flows through resistor R2?
Using the relation from question 1:
I2 = (R1 / R2) × I1
Without the value of I1, we cannot compute I2 directly.
4) What is RX, the value of the unknown resistor RX?
To find RX, we would need to analyze the circuit further, considering the paths and applying Kirchhoff’s laws. However, without a circuit diagram or additional information, we cannot determine RX.
5) What is V1, the magnitude of the voltage across resistor R1?
As established, V1 = V2. Without the value of I1, we cannot compute V1 directly.
Explanation:
In this circuit, the fact that no current flows through R4 (I4 = 0) indicates that there is no voltage difference across it. This means the points at both ends of R4 are at the same potential. Consequently, the voltage drop across R1 must equal the voltage drop across R2. Using Ohm’s Law, this leads to the relation I1 × R1 = I2 × R2, allowing us to express I2 in terms of I1. However, to find the exact values of currents and voltages, we need to know the total resistance in the circuit and the configuration of the resistors, which requires a circuit diagram or additional information. Without this, we cannot proceed with precise calculations.
Understanding these relationships is crucial in circuit analysis, as they allow us to simplify complex circuits and determine unknown values using known quantities and fundamental laws like Ohm’s Law and Kirchhoff’s laws.