kirchhoffs-laws
I’ve just started an engineering course, and my 1st module is electrical engineering. Unfortunately my teacher is a 100 years old and hasn’t explained Kirchoff’s law to us in an understanding manor. In this question I’ve been asked to find the voltage across each resistor. Please could someone explain to me how this is done. The simpler the explanation the better, I honestly won’t find it patronising, it would be a great help.
Thanks in advance
Kirchhoff's current law (KCL): the sum of the currents in a node is zero.
Say you have 5 wires coming together in a node as shown, and \$I_1\$, \$I_3\$ and \$I_4\$ supply current to the node. This current has to go somewhere, and will go from the node by \$I_2\$ and \$I_5\$:
\$ I_2 + I_5 = I_1 + I_3 + I_4 \$
such that
\$ I_1 - I_2 + I_3 + I_4 - I_5 = 0 \$
(The minus signs for \$I_2\$ and \$I_5\$ are due to the reversed arrows for those currents.)
A more general form of KCL says that the current entering a closed boundary is equal to the current leaving it:
Kirchhoff's voltage law (KVL): the sum of the voltages in a closed circuit is zero. If you have a circuit consisting of a battery and a resistor as a load then the voltage over the resistor is \$\mathrm{-V_{bat}}\$ (the minus sign means that if you go clockwise through your circuit you go from \$-\$ to \$+\$ for the battery, but from \$+\$ to \$-\$ for the resistor).
Total voltage: \$\mathrm{+V_{bat} - V_{bat} = 0}\$.
This goes for every closed loop path you can find in a design, no matter how complicated and how many branches there are.
Why is that Kirchhoff's voltage and current law always give answer?
They don't always give answer. For example:
simulate this circuit – Schematic created using CircuitLab
KVL applied to the above gives:
$$1V = 2V$$
which is a contradiction.
Another example:
KCL applied to the above gives:
$$1A = -2A$$
which is a contradiction.
Another example:
KCL applied to the above gives
$$\frac{V}{1 \Omega} = \frac{V}{1 \Omega}$$
so the voltage and current are undetermined.
The fact is, it is possible to draw an ideal circuit schematic that is inconsistent or has undetermined voltages or currents.
Furthermore, node voltage analysis relies on KCL while mesh current analysis relies on KVL so I don't quite understand the 2nd part of your question.
Best Answer
Kirchoff's laws don't all need to be used to solve one circuit. You can go with Kirchoff's nodal analysis (KCL), or Kirchoff's Voltage law (KVL)
Kirchoff's nodal analysis (KCL):
Sum of the currents going into a node equals the sum of the currents coming out.
So.. Let us assign a variable name to (i.e. Vx, Va) to any connection with more than 2 ends. So assign Vx to that node on the top. Then you need to characterize the algebra problem by defining each current and how they equal relative to each other using this law.
Then try to analyze the currents across each branch with respect to Va and to ground or voltage source that is in series.
Kirchoff's Voltage law (KVL):
Sum of voltages in a loop sum up to zero.
A loop in this context is a series of circuit components whose path starts at a source path and leads down back to the that source path, path = < c1, c2, c3, c1 > (where cx = component x) (i.e. 10V, 5Ohm, 10Ohm, back to 10V)
So.. assign all existing current loops, i.e. left loop can be Current 1, I1 right loop can be current 2, I2 and the current going down between the two (current 3, I3) is a mix of the two, which relatively depends on the direction assigned to each current (I1, and I2)
Then you need to characterize the algebra problem to find the voltage across each component in each loop.