Question

What is the PD across the 6 ohms resistor?

Answer 1

In the above question, we were given three resistors, two are connected in parallel and one is connected in series with the parallel unit. So, we need to find the total current and next, find the voltage across parallel ones easily.

Complete step by step answer:
In the question, let us write down the given terms,
$\begin{aligned} & {{R}_{1}}=4\Omega ,{{R}_{2}}=3\Omega ,{{R}_{3}}=6\Omega \\\ & V=12V \\\ \end{aligned}$
Let us find the total current through the circuit,
The total current is calculated by dividing the total voltage with effective resistance.
$\begin{aligned} & {{R}_{eff}}=4\Omega +\dfrac{3\times 6}{3+6} \\\ & \Rightarrow {{R}_{eff}}=6\Omega \\\ \end{aligned}$
Now, the current through the circuit will be,
$\begin{aligned} & i=\dfrac{V}{{{R}_{eff}}} \\\ & \Rightarrow i=2A \\\ \end{aligned}$
As parallel combined quantities have same voltage,
$\begin{aligned} & {{V}_{6\Omega }}=2A\times 2\Omega \\\ & \therefore{{V}_{6\Omega }}=4V \\\ \end{aligned}$
Therefore, we should calculate the unknown voltages in such cases.

Additional information:
Resistor circuits that combine series and parallel resistors networks together are generally known as Resistor Combination or mixed resistor circuits. The method of calculating the circuit's equivalent resistance is the same as that for any individual series or parallel circuit and hopefully we now know that resistors in series carry exactly the same current and that resistors in parallel have exactly the same voltage across them. Electrical current is the flow of charged particles. The flow of charges will be constant in current electricity. Electric current flows from higher electric potential to lower electric potential. For the current to flow, it requires a circuit which is a closed loop of a conducting material. The circuit consists of wires which are connected end to end and the electrons flow in the same direction.

Note:
In the above question, we need to keep in mind that the resistors connected in parallel have the same voltage. When the resistors are connected in series, the current flowing through the resistors is the same. But the voltage of the two resistors could be different.