# Kirsof Tensions Law

The Kirchhoff Voltages Act (KVL) is Kirchhoff's second law dealing with the conservation of energy around a closed circuit pathway.

**Gustav Kirchhoff's Law of Voltages**is the second of the basic laws that we can use for circuit analysis.Voltage law specifies that for a closed loop **path, the algebraic sum of all voltages around any closed loop in a circuit is equal to zero.**This is because a circuit cycle is a closed conductive path, so there is no loss of energy.

In other words, the algebraic sum of all potential differences around the loop should be equal to zero as follows: ΕV = 0 .Note here that the term "algebraic sum" means taking into account the poles and signs of resources and voltage drops around the cycle.

Kirchhoff's idea, commonly known as **Energy Conservation,** is that when you move around a closed loop or circuit, you go back to where you started in the circuit, and therefore return to the same initial potential without losing voltage around the loop.Therefore, any voltage drop around the loop should be equal to any voltage source encountered along the way.

Therefore, when applying the Kirsof voltages law to a particular circuit element, it is important that we pay special attention to the algebraic signs ( + and – ) of voltage drops between the elements and the emks of resources, otherwise our calculations may be incorrect.

But before we take a closer look at the Kirsof voltages law (KVL), let's understand the voltage drop on a single element, such as resistance.

### Single Circuit Element

For this simple example, we will assume that the current is in the same direction as the flow of the I positive charge, that is, the traditional current flow.

Here, the flow of the current through the resistance is from point A to point B, that is, from the positive terminal to the negative terminal.Therefore, as we move in the same direction as the current flow , there will be a potential *decrease* in the resistance element, which will lead to a -IR voltage drop on it.

If the current flow was in the opposite direction from point B to point A, then there would be an *increase* in potential throughout the resistant element as it moves from a – potential to a + potential, giving us a +I*R voltage drop.

Therefore, in order to correctly apply Kirchhoff's voltage law to a circuit, we must first understand the direction of polarity, and as we can see, the sign of voltage drop through the resistant element will depend on the direction of the current passing through it.As a general rule, you lose potential in the same current direction throughout an element and gain potential as you move in the direction of an EMF source.

It can be assumed that the direction of the current around a closed circuit is clockwise or counterclockwise, and one of them can be selected.If the chosen direction differs from the actual direction of the current, the result will still be correct and valid, but it will cause the algebraic answer to have a minus sign.

To understand this idea a little more, let's look at a single circuit cycle to see if the Kirsof Voltages Act is correct.

### Single Circuit Cycle

The law on kirsof voltages states that the algebraic sum of potential differences in any cycle should be equal to zero: ΕV = 0. Since the two resistors, R1 and R2, are connected in a series connection, they are both part of the same cycle, so the same current must flow from each resistance.

Thus, voltage drop along resistance, voltage drop throughout R _{1} = I*R _{1} and voltage drop along resistance are given by R _{2} = I*R _{2} KVL:

In this single closed loop, we can see that applying Kirchhoff's Voltage Law produces the equivalent or total resistance formula in the serial circuit, and we can expand it to find the values of voltage drops around the loop.

### Kirsof Tensions Law Question Example 1

Three value resistances: 10 ohm, 20 ohm and 30 ohm respectively, connected in series throughout a 12-volt battery supply.

a) total resistance, B) circuit current, C) current in each resistance, d) Voltage Drop in each resistance, e) Calculate that Kirchhoff's voltage law kvl is correct.

### a) Total Resistance ( R_{T} )

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

Then the total circuit resistance is equal to R _{T} , 60Ω

### b) Circuit Current (I)

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

### c) Current Passing Through Every Resistance

Resistances are serially connected, they are all part of the same cycle, and therefore each overflows with the same amount of current.So:

I _{R1} = I _{R2} = I _{R3} = I _{SERIES} = 0.2 amps

### d) Voltage Drop Through Each Resistance

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 Rx _{3} = 0.2 x 30 = 6 volts

### e) Kirsof Voltages Law Verification

Thus, the law of Kirsof voltages applies because it is as accurate as the sum of individual voltage drops around the closed loop.

### Kirchhoff's Circuit Cycle

Here we saw that Kirchhoff's law of voltages, KVL is Kirchhoff's second law, and when you move a closed circuit from a fixed point back to the same point and take into account the polarity, the algebraic sum of all voltage drops is always zero, that is, ΕV = 0.

The theory behind Kirchhoff's second law is also known as the law on the protection of voltage, which is especially useful when dealing with serial circuits, since serial circuits also function as voltage dividers, and the voltage divider circuit is an important application of many series.