What is KVL ( Kirchhoff’s Voltage Law )
- KVL ( Kirchhoff’s Voltage Law ), also known as the second rule of Kirchhoff’s, explains that the sum of voltages in an enclosed circuitry is always equal to 0.
- KVL applied for voltage measurement in circuits. To explain it we discuss given circuitry.
- As you can see in a given circuit that the single voltage source is linked with the passive elements (the electric element which does not produce power like a resistor), which have (b,c,d,e,f) voltage about them.
- As all these elements are connected in series so there voltages values will be added.
- If we apply KVL (Kirchhoff’s voltage law) which says voltage around the passive (the electric element which does not produce power, like a resistor) element in circuitry always equivalent and reverse to source voltage.
- Therefore, the summation of the voltage changes across all the elements in circuitry is always equated to 0.
What is Mesh Analysis
- It is the method to helps us to find the current and voltage in any close-loop working with the KVL, by this analysis we can find values of current and voltage across any component of the loop on the circuit.
- There are three steps to apply this mesh analysis. Which described here.
- Allocate discrete current values to every enclosed circle of the network.
- After that Apply Kirchoff voltage law about every enclosed circle of the system.
- And resolve the resultant concurrent linear equations to find the value of current in the ring.
Example of Mesh AnalysisNow we practically discuss the Mesh Analysis by the given example.
- Let's suppose that we have a given circuit diagram which has two loops and we have to apply mesh rule on this circuit.
- The values of the elements of this circuit which we know are given below.
- (R1)= (5 ohms)
- (R2) = (6 Ohm)
- (R3)= (10 ohms)
- (V1) = (12 volts)
- (V2)= (8 volts)
- To apply mesh rule on this circuit, first of all, we recognize the direction of the current flowing in these two loops.
- In the first loop which is (ABEF) the direction of current is clock-wise and it is represented as (I1).
- In the second loop which is (BCDE) the direction of current (I2) is also clockwise.
- Now applying kVl to write the equation for both of these two loops.
(V1)= (R1I1)+ R3(I1 - I2)
- This equation can also be written as
(V1)= (R1 +R3)I1-R3I2 – (A)
- Now if we apply KVL on loop 2 then we have this equation.
(V2) = (R2I2) + (R3)(I2-I1)
- It can also be written as
(V2) = (R2+R3)I2 –(R3I1) – (B)
- Now we will put the values of given parameters of circuit and find the value of the unknown parameter.
(12) = (5+10)(I1)- (10)I2
12= (15I1)- (10I2) –(C)
- When we put value in equation B it will become
(8)= (6+10)(I2)- (10)(I1)
8=16 (I2)-10(I1) –(D)
- By solving equation C and D we have.
I1= 1.94 A
Example of KVL ( Kirchhoff’s Voltage Law )
- In the given diagram, a circuit is drawn at which we have to apply KVL.
- In this circuit, there are three loops which are labeled in the circuit by no 1, 2, 3.
- We will apply KVL on these three loops one by one and will get correspondent equations.
- When we apply KVL to the first loop we get this equation.
V1= (I1 x R1) + R3(I1+I2)
10= (I1 x10) + 40(I1+I2)
10= 50 I1 + 40 I2
- After applying KVL on the first loop we now apply it on the second loop then we get an equation for this loop.
V2= (I2 x R2) + R3(I1+I2)
20= (I2 x 20) + 40(I1+I2)
20 = 40 I1+ 60I2
- After findng equations for loop first and second now we find the equation for the third loop.
V1-V2 = (I1 x R1) – (I2 x R2)
(10-20) = (10I1) – (20I2)
- By solving equations of loop one and second we get the value of (I1) and (I2) which are mention below.
I1= -0.143 A
I2= +0.429 A
- By using the value of I1 and I2 now we find the value of current I3.
(I3 = I1 + I2)
- Putting the value of I1 and I2 we get current at resistance (R3).
I3 = -0.143 + 0.429 = 0.286 A
- I3 is the current which is passing through the resistance (R3), we can also find the value of voltage across this resistance by using I3.
V3= (0.286 x 40) = 11.44 V
Applications of KVL Law
- These are some important applications of KVL law.
- Kirchhoff’s laws are used to measure the unknown standards such as current (I), Voltage (V), also the direction of moving current in the circuit.
- This rule is applicable to every circuit but it is very fruitful to solve complicated circuitries.
- This law also helps us to observe the transferal of power in the circuit.