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PGCIL DT Electrical 13 Aug 2021 Official Paper (NR I)

Option 1 : Kirchhoff’s voltage law

__Kirchhoff’s Voltage Law (KVL): __It states that the algebraic sum of all voltage around a close path or loop is zero.

Mathematically, KVL implies that

\(\mathop \sum \limits_{m = 1}^M {v_m} = 0 \)

Where M is the number of voltages in a loop or number of branches in a loop

And, vm is mth voltage.

Consider a circuit shown below in which R1 and R2 are two resistance, v1, v2 are two voltage source which causes current (I) flow in the loop.

The sign of voltage drop across the passive element is such a way that the current entering from the positive terminal.

Applying KVL on this circuit

V1 + V4 – IR1 – IR2 = 0

Or, V1 + V4 = IR1 + IR2

Hence, the Sum of Voltage drops = Sum of Voltage rises

Note: KVL deals with the conservation of energy.

__Additional Information__

__Kirchhoff’s Current Law (KCL):__ It states that the algebraic sum of currents entering a node or closed boundary is zero.

Mathematically, KCL implies that

\(\mathop \sum \limits_{n = 1}^N {i_n} = 0 \)

Where N is the number of branches connected to the node

And in is the nth current entering or leaving the node.

By this law current entering a node may be regarded as positive and current leaving a node may be regarded as negative or vice-versa.

Considered the node in the figure shown below, in which i1, i3, and i5 are incoming current and i2, i4, and i6 are outgoing current.

Applying KCL gives,

i1 + i3 + i5 = i2 + i4 + i6

Hence, the sum of currents entering a node is equal to the sum of the currents leaving the node.

Note: KCL is based on the conservation of charge.