COMPUTE THE VOLTAGE ACROSS A RESISTOR
Determine the voltage Vx across R4
SOLUTION
To know the voltage across R4, we can proceed by calculating the current flowing through R4. In this way, by means of Ohm’s law we can then calculate the value of the voltage across R4.
To quickly solve the circuit, it is convenient to redesign it so as to highlight that the resistors R1 and R2 are connected in parallel.
The overall value of their resistance is equal to:
We also note that resistors R3 and R4 are connected in series. The overall value of their resistance is equal to:
We thus obtain the following equivalent circuit which allows us to calculate what the current flowing in the resistor R34.
We use the current divider formula:
And we thus obtain that I34 = 1 A
We can now return to the starting circuit and indicate the value of the current that circulates in the branch of resistors R3 and R4.
We are now able to apply Ohm’s law at the resistor R4.
In particular, we know that the current entering R4 which we denote by I4 = -I34 = -1 A. Knowing the value of R4 = 6 Ohm, we have that:
Ultimately, the voltage Vx across R4 is equal to -6 V.
