Categories Basic Law Electrical

# The Kirchhoff’s Voltage Law(KVL)

Kirchhoff’s voltage law, States that the sum of all-around any closed loop in a circuit must equal zero.

## THE kirchhoff’s voltage law(KVL) CIRCUIT:

The principle known as Kirchhoff’s Voltage Law in 1847 by Gustav R. Kirchhoff, a German physicist, can be stated as such:

“The algebraic sum of all voltages in a loop must equal to be zero

This is as a result of a circuit loop may be a closed conducting path, thus no energy is lost.

Mathematically, ΣV = 0.

### Kirchhoff’s Voltage Law Example, No1:

Three resistors of values: 20 ohms, 30 ohms, and 40 ohms, respectively are connected in series across a 24-volt battery supply. Calculate: a)  total resistance, b)  circuit current, c)  current through each resistor, d)  voltage drop across each resistor, e) verify that Kirchhoff’s voltage law, KVL holds true.

Solution:

#### a) Total Resistance (RT):

RT = R1 + R2 + R3  =  20Ω + 30Ω + 40Ω = 90Ω

Then the total circuit resistance RT is equal to 90Ω.

#### b) Circuit Current (I):

Thus the total circuit current is equal to 0.26 amperes.

#### 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:

IR1 = IR2 = IR3 = ISERIES  =  0.26 amperes

#### d) Voltage Drop Across Each Resistor:

VR1 = I x R1 = 0.267 x 20  =  5.34 volts

VR2 = I x R2 = 0.267 x 30  =  8.01 volts

VR3 = I x R3 = 0.267 x 40  =  10.68 volts

#### e) Verify Kirchhoff’s Voltage Law:

Thus (kvl) holds true as the individual voltage drops around the closed loop add up to the total.

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