Question

What is the power consumed across AB?

A)2W
B)4W
C)6W
D)8W

Answer 1

Let us first find the equivalent resistance cross the terminals AB. Next, keep us finding the power formula in terms of current flowing through the circuit and the equivalent resistance through the circuit. Power is equal to resistance times the square of the current flowing through the circuit.

Formula used:
$P={{i}^{2}}R$

Complete step by step answer:
In the above figure, a total of five resistors are placed at different locations in the terminal AB. Now, we need to find the equivalent resistance of the given five resistors.
Let us divide it into two parts. The above part consists of three resistors and the below part consists of two resistors.
Now, we need to find the effective resistance of the above part,
$\begin{aligned} & {{\operatorname{R}}_{eq}}=\dfrac{\dfrac{{{r}_{1}}{{r}_{2}}}{{{r}_{1}}+{{r}_{2}}}\times {{r}_{3}}}{\dfrac{{{r}_{1}}{{r}_{2}}}{{{r}_{1}}+{{r}_{2}}}+{{r}_{3}}} \\\ & \Rightarrow {{R}_{eq}}=\dfrac{7\times 7}{21} \\\ & \therefore {{R}_{eq}}=\dfrac{7}{3} \\\ \end{aligned}$
Next, the above obtained resistance is in series with the adjacent resistor and parallel to the below traitor.
Therefore, the net effective resistance will b,
$\begin{aligned} & {{R}_{eq}}=\dfrac{7}{3}+7=\dfrac{28}{3} \\\ & \Rightarrow {{R}_{eff}}=\dfrac{\dfrac{28}{3}\times 7}{\dfrac{49}{3}} \\\ & \therefore {{R}_{eff}}=4\Omega \\\ \end{aligned}$
Therefore, the power through the terminal AB will be,
$\therefore P=1\times 4=4W$
Therefore, the correct option is option C.

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. Resistors can be connected in series connection alone or in parallel connection alone. Some resistor circuits are made from a combination of series and parallel networks to develop more complex circuits. These circuits are generally known as Mixed Resistor Circuits. Even though these circuits have combined series and parallel circuits, there is no change in the method of calculating the Equivalent Resistance. The basic rules of individual networks like “same current flows through resistors in series” and “voltage across resistors in parallel is same” are applicable to mixed circuits.

Note:
In the series combination of resistance, the net current flowing through the circuit will be the same. Whereas in the case of parallel combination of circuits, the net voltage flow through the circuit will be the same. Therefore, be sure while solving the series and parallel combination of circuits.