Question

Select the expressions that will be equal to the voltage of the battery in the circuit, where V_A, for example, is the potential drop across resistor A.

Check all that apply.

A) \(V_{\mathrm{A}}+V_{\mathrm{B}}\)

B) \(V_{\mathrm{A}}+V_{\mathrm{C}}\)

C) \(V_{\mathrm{B}}+V_{\mathrm{C}}\)

D) \(V_{\mathrm{A}}+V_{\mathrm{B}}+V_{\mathrm{C}}\)

E) \(V_{\mathrm{A}}+V_{\mathrm{B}}+V_{\mathrm{C}}+V_{\mathrm{D}}\)

F) \(V_{\mathrm{A}}+V_{\mathrm{D}}\)

G) \(V_{\mathrm{D}}\)

Answer 1

Concepts and reason

The main concepts required to solve the problem are the Kirchhoff’s voltage law and Ohm’s law.

For the calculation of the voltage drop across the resistor first calculate the current flow in the circuit and from Ohm’s law the voltage drop across the resistor can be determined.

Fundamentals

From Ohm’s law the expression of the voltage is express as follows,

$V = IR$

Here, $V$ is the voltage, $I$ is the current and $R$ is the equivalent resistance in the circuit.

Form Kirchhoff’s voltage law the summation of the voltage in a closed loop is equal to zero,.

$\sum {{V_{enclosed}}} = 0$

The circuit diagram for the system equation is provided below.

Apply KVL in loop $\;ada$ ,

$\begin{array}{c}\\ - V + {V_A} + {V_B} = 0\\\\V = {V_A} + {V_B}\\\end{array}$

Apply KVL in loop $aeda$

$\begin{array}{c}\\ - V + {V_A} + {V_C} = 0\\\\V = {V_A} + {V_C}\\\end{array}$

.

Apply KVL in loop $abcda$ ,

$\begin{array}{c}\\ - V + {V_D} = 0\\\\V = {V_D}\\\end{array}$

Ans:

The source voltage across the battery is equal to, ${V_A} + {V_B},\,{V_A} + {V_C},{\rm{ and }}{V_D}$ .