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 find the voltage Vx in the given circuit, we can use the voltage divider rule. The voltage divider rule states that the voltage across a resistor in a series circuit is proportional to the resistance of that resistor compared to the total resistance of the circuit.
Here are the steps to calculate Vx:
Step 1: Calculate the total resistance of the circuit (Rt) by combining resistors R1, R2, R3, and R4. Since these resistors are in series, their resistances simply add up:
Rt = R1 + R2 + R3 + R4
In this case, Rt = 13.0kΩ + 4.0kΩ + 13.0kΩ + 21.0kΩ = 51.0kΩ
Step 2: Calculate the voltage across Vx using the voltage divider rule:
Vx = (R4 / Rt) * V
In this case, Vx = (21.0kΩ / 51.0kΩ) * 17.0V
Step 3: Perform the calculation to find the value of Vx:
Vx = (0.4118) * 17.0V
Vx ≈ -6.97V
Hence, the voltage Vx is approximately -6.97 Volts.
To find the voltage Vx in the given circuit, you can use the concept of voltage division. Here are the steps to calculate Vx:
Step 1: Identify the circuit elements and their values:
- V = 17.0 Volts (supply voltage)
- R1 = 13.0 k ohms (resistance connected to V)
- R2 = 4.0 k ohms (resistance connected between R1 and Vx)
- R3 = 13.0 k ohms (resistance connected between Vx and ground)
- R4 = 21.0 k ohms (resistance connected between R3 and ground)
Step 2: Calculate the total resistance in the path from V to ground:
- R_total = R1 + R2 + R3 + R4
- R_total = 13.0 k ohms + 4.0 k ohms + 13.0 k ohms + 21.0 k ohms
- R_total = 51.0 k ohms
Step 3: Apply voltage division formula:
- Vx = V × (R3 / R_total)
- Vx = 17.0 V × (13.0 k ohms / 51.0 k ohms)
- Vx = 17.0 V × (0.2549)
- Vx = 4.3343 V
Therefore, the voltage Vx is approximately 4.33 Volts.