Kirchhoffs Voltage Law (KVL) is Kirchhoff’s second law that deals with the conservation of energy around a closed circuit path.

## Kirchhoffs Voltage Law

Gustav Kirchhoff‘s Voltage Law constitutes one of the fundamental principles applicable to circuit analysis. According to this law, within a closed loop series path in a circuit, the sum of all voltages around the loop equals zero. This fundamental property arises from the fact that a circuit loop represents a closed conducting pathway wherein energy conservation prevails, ensuring no loss of energy.

In essence, the algebraic sum of all potential differences around the loop must equate to zero (ΣV = 0), considering the polarities and signs of both sources and voltage drops within the loop.

Kirchhoff’s concept embodies the principle of Conservation of Energy, elucidating that traversing a closed loop circuit leads back to the initial potential point without any loss of voltage. Consequently, any voltage drops encountered around the loop must balance out with the voltage sources encountered.

Therefore, when applying Kirchhoff’s voltage law to analyze specific circuit elements, meticulous attention must be given to the algebraic signs (+ and -) of voltage drops across elements and the electromotive forces (EMFs) of sources to ensure accurate calculations.

Before delving deeper into Kirchhoff’s voltage law (KVL), it is imperative to grasp the concept of voltage drop across individual circuit elements, such as resistors.

### A Single Circuit Element

In this straightforward illustration, let’s assume that the current, denoted as *I*, aligns with the positive charge’s flow, adhering to conventional current flow principles.

In the scenario presented, the current moves through the resistor from point A to point B, from the positive to the negative terminal. Consequently, as we travel in tandem with the current’s direction, a decrease in potential occurs across the resistive component, resulting in a negative voltage drop of −*IR*.

Had the current flowed in the opposite direction, from point B to point A, a rise in potential across the resistor would ensue, transitioning from a negative potential to a positive one, yielding a positive voltage drop of +*IR*.

Therefore, for the accurate application of Kirchhoffs voltage law within a circuit, understanding the polarity’s orientation is crucial. Notably, the voltage drop’s sign across the resistive element hinges on the current’s direction traversing it. As a general guideline, potential diminishes in the direction of current flow across an element and increases towards an electromotive force (emf) source.

In a closed circuit, the direction of current flow may be presumed either clockwise or counterclockwise, with either choice being acceptable. Deviating from the actual current flow’s direction will yield a valid but negated algebraic result.

To further grasp this concept, let’s examine a single circuit loop to ascertain the validity of Kirchhoffs Voltage Law.

### A Single Circuit Loop

According to Kirchhoff’s voltage law, the total sum of potential differences within any loop equals zero (ΣV = 0). Given that resistors R1 and R2 are interconnected in a series configuration, they form a single loop, necessitating identical currents flowing through each resistor.

Consequently, the voltage drop across resistor R1 equals *I*×*R*_{1}, while the voltage drop across resistor R2 equals *I*×*R*_{2}, as per Kirchhoffs Voltage Law (KVL):

**V _{s} + (-IR_{1}) + (-IR_{2}) = 0**

∴ **V _{s} = IR_{1} + IR_{2}**

**V _{s} = I(R_{1} + R_{2}**)

**V _{s} = IR_{T} **Where,

**R**=

_{T}**R**

_{1}+ R_{2}Utilizing Kirchhoffs Voltage Law in this solitary closed loop leads to the derivation of the formula for the total resistance within the series circuit. Furthermore, this approach can be extended to ascertain the magnitudes of the voltage drops across the loop.

\mathbf{R_T = R_1 + R_2}

\mathbf{I = \frac{V_S}{R_T} = \frac{V_S}{R_1 + R_2}}

\mathbf{V_{R1} = IR_1 = V_S \left[ \frac{R_1}{R_1 + R_2} \right ] }

\mathbf{V_{R2} = IR_2 = V_S \left[ \frac{R_2}{R_1 + R_2} \right ] }

### Kirchhoff’s Voltage Law Example No1

Three resistor of values: 10 ohms, 20 ohms and 30 ohms, respectively are connected in series across an ideal 12 volt DC battery supply. Calculate: a) the total resistance, b) the circuit current, c) the current through each resistor, d) the voltage drop across each resistor, e) verify that Kirchhoff’s voltage law, KVL holds true.

**a) Total Resistance (R _{T})**

R_{T} = R_{1} + R_{2} + R_{3} = 10Ω + 20Ω + 30Ω = 60Ω

Then the total circuit resistance R_{T} is equal to 60Ω

**b) Circuit Current (I)**

Thus the total circuit current I is equal to 0.2 amperes or 200mA

**c) Current Through Each Resistor**

The resistors are wired together in series, they are all part of the same loop and therefore each experience the same amount of current. Thus:

I_{R1} = I_{R2} = I_{R3} = I_{SERIES} = 0.2 amperes

**d) Voltage Drop Across Each Resistor**

V_{R1} = I x R_{1} = 0.2 x 10 = 2 volts

V_{R2} = I x R_{2} = 0.2 x 20 = 4 volts

V_{R3} = I x R_{3} = 0.2 x 30 = 6 volts

**e) Verify Kirchhoff’s Voltage Law**

Thus Kirchhoff’s voltage law holds true as the individual voltage drops around the closed loop add up to the total.

### Kirchhoff’s Circuit Loop

Here, we’ve observed Kirchhoff’s second law, known as Kirchhoffs Voltage Law (KVL), which dictates that the algebraic sum of all voltage drops across a closed circuit, accounting for polarity, invariably amounts to zero (**ΣV = 0**).

This principle, synonymous with the conservation of voltage, proves especially beneficial in analyzing series circuits. Notably, series circuits function as voltage dividers, with the voltage divider circuit serving as a significant application of various series configurations.

Read more Tutorials on DC Circuits | |
---|---|

1. | DC Circuit Theory |

2. | Ohms Law and Power |

3. | Electrical Units of Measure |

4. | Kirchhoffs Circuit Law |

5. | Kirchhoffs Current Law |

6. | Kirchhoffs Voltage Law |

7. | Mesh Current Analysis |