In the circuit shown, find the voltage Vx (in Volts) if V = 17.0 Volts, R1 = 13.0 k ohms, R2 = 4.0 k ohms, R3 = 13.0 k ohms and R4 = 21.0 k ohms.
Answer is -6.5 I don't understand how they got it, can someone please explain it with steps? Thanks
tinypic. c o m/r/2pzhcpl/8
To get help, You will have to explain how the resistors are connected and
identify Vx.
To find the voltage Vx in the given circuit, we can use the concept of voltage division.
Voltage division refers to the distribution of voltage across different resistors in a series circuit. The voltage across a resistor is proportional to its resistance compared to the total resistance in the circuit.
Here are the steps to find Vx:
Step 1: Calculate the equivalent resistance, Req, of R3 and R4 in parallel. Since these resistors are in parallel, we can calculate Req using the formula:
1/Req = 1/R3 + 1/R4
Substituting the given values:
1/Req = 1/13.0k + 1/21.0k
Calculating the reciprocal:
1/Req = (21.0k + 13.0k) / (13.0k * 21.0k)
Simplifying:
1/Req = 34.0k / (13.0k * 21.0k)
Taking the reciprocal of both sides:
Req = (13.0k * 21.0k) / 34.0k
Calculating:
Req = 8.14k ohms
Step 2: Calculate the equivalent resistance, Reqs, of R2 and Req in series. Since these two resistors are in series, we can simply add their resistances:
Reqs = R2 + Req
Reqs = 4.0k + 8.14k
Reqs = 12.14k ohms
Step 3: Use the voltage division formula to find Vx. The voltage across R1 is the difference between V and Vx, and it is proportional to the resistance ratio:
(V - Vx) / R1 = Vx / Reqs
Cross-multiplying:
Reqs * (V - Vx) = R1 * Vx
Expanding:
12.14k (V - Vx) = 13.0k * Vx
Rearranging the equation to solve for Vx:
12.14kV - 12.14kVx = 13.0kVx
Combining like terms:
12.14kV = 25.14kVx
Dividing both sides by 25.14k:
Vx = (12.14kV) / 25.14k
Calculating:
Vx ≈ -6.49 Volts
Therefore, the voltage at Vx is approximately -6.49 Volts.