Question

Which equation represents Kirchoff’s second law?

Answer 1

Kirchhoff's Law, often known as Kirchhoff's Law of Circuits, is a mathematical equation that deals with resistance, current, and voltage in the lumped element model of electrical circuits. Circuit theory is based on these laws. They monitor the flow of current and the changes in voltage in a circuit's loop. German physicist Gustav Robert Kirchhoff provided the fundamental knowledge of electrical circuits.

Complete step by step solution:
Kirchoff’s second law:
“For every closed network, the voltage surrounding a loop equals the sum of all voltage drops in the same loop, and it also equals zero.”
It represents the equation $\sum V = 0$.
Explanation:
The Voltage Law of Gustav Kirchhoff is the second of his fundamental laws that we can apply for circuit analysis. His voltage law asserts that the algebraic sum of all the voltages around any closed loop in a circuit is zero for a closed-loop series path. This is because a circuit loop has a closed conducting line, which means that no energy is lost.
To put it another way, the algebraic sum of ALL potential differences around the loop must equal zero, as follows: $\sum V = 0$. It's worth noting that the phrase "algebraic sum" refers to accounting for the polarities and signs of the sources as well as voltage dips along the loop.
The Conservation of Energy is a notion proposed by Kirchhoff that states that traveling through a closed-loop, or circuit, will return you to where you started in the circuit and hence to the same beginning potential with no voltage loss. As a result, any voltage drops encountered along the way must be equal to any voltage sources encountered.
When applying Kirchhoff's voltage law to a given circuit element, it's critical to pay close attention to the algebraic signs, ($+$ and $-$), of voltage drops across elements and source EMFs, or our calculations will be incorrect.
But, before diving into Kirchhoff's voltage law (KVL), it's important to understand the voltage drop across a single element, such as a resistor.

Note: Example of Kirchhoff's Voltage Law:
Three resistors of $10$ ohms, $20$ohms, and $30$ ohms are linked in series across a $12$volt battery supply, accordingly. Calculate: a) total resistance, b) circuit current, c) current through each resistor, d) voltage drop across each resistor, e) Kirchhoff's voltage law, KVL.:
Total Resistance$({R_T})$:
${R_T}\; = \;{R_1}\; + \;{R_2}\; + \;{R_3}\; = \;10\Omega \; + \;20\Omega \; + \;30\Omega \; = \;60\Omega$
Then the total circuit resistance $({R_T})$is equal to $60\Omega$.
Circuit Current $\left( I \right)$:
$I = \dfrac{{{V_S}}}{{{R_T}}} = \dfrac{{12}}{{60}} = 0.2A$
As a result, the total circuit current$\left( I \right)$ in $0.2$ amperes $\left( {200mA} \right)$.
Current Through Each Resistor:
Because the resistors are connected in series and are all part of the same loop, they all get the same amount of current. Thus,
${I_{R1}}\; = \;{I_{R2}}\; = \;{I_{R3}}\; = \;{I_{SERIES}}\; = \;\;0.2{\text{A}}$
Voltage Drop Across Each Resistor:
${V_{R1}}\; = \;I\; \times {R_1}\; = \;0.2\; \times 10\;\; = \;\;2{\text{ }}volts$
${V_{R2}}\; = \;I\; \times {R_2}\; = \;0.2\; \times 20\;\; = \;\;4{\text{ }}volts$
${V_{R3}}\; = \;I\; \times {R_3}\; = \;0.2\; \times 30\;\; = \;\;6volts$
Verify Kirchhoff’s Voltage Law:
${V_S} + ( - I{R_1}) + ( - I{R_2}) + ( - I{R_3}) = 0$
$12 + ( - 0.2 \times 10) + ( - 0.2 \times 20) + ( - 0.2 \times 30) = 0$
$12 + ( - 2) + ( - 4) + ( - 6) = 0$
Therefore,
$12 - 2 - 4 - 6 = 0$
As the various voltage decreases around the closed-loop add up to the total, Kirchhoff's voltage equation holds true.