DC Circuit Analysis Flashcards
What happens to a metals resistivity when you increase temp?
Why?
The resistivity increases.
Because the crystal lattice of ions vibrates more if the metal is heated, increasing amount of electron scattering, which destroys current/
What effect do impurities have on resistivity?
Electrons scattering of impurities and/or defects in the lattice also destroys.
So impure metal will have larger resistivity than a pure metal. These impurities add a temp independent offset to the resistivity which depends on the impurity/defect concentration.
How does the resistivity change with temp in a semiconductor?
The resistivity decreases at higher temp, as more electrons are able to carry current as more electrons and holes are able to carry current when electrons get thermally excited across the energy gap.
At absolute zero silicon is an insulator.
State Ohm’s law exactly.
Ohm’s law states that in an ideal conductor the current flowing between 2 points is directly proportional to the P.D.
Equations for power dissipation
And what is important to remember about them?
You have to be careful using these expressions.
For the equation P = I2R, power can only be proportional to resistance if the current through the resistor is constant
For P = V2/R, power can only be inversely proportional to resistance if the voltage across the resistor is constant.
Max Power Transfer Theorem Relationship
RL = RS
What are the two misconceptions about the max power theorem?
- ” RL = RS means you need to choose a source resistance to match the load resistance”
- This is not** right as it assumes you have a **given source that is constant and are choosing the best load for it. If you increase RS you clearly increase the current and as a result the power transferred. So if a load has been given, to maximise power transferred, the source load needs to be minimised as much as possible.
- “The power transferred being maximised means the voltage VL delivered across the load is maximised.”
- You can recognize that this is wrong when you see that the circuit is just a potential divider. The voltage across VL is actually maximised when RL>>RS so the voltage across the load is equal to the voltage of the source. Not when RL = Rs which instead gives VL = VS / 2.
Kirchoff’s First Rule (The Current Law)
The law states that the algebraic sum of currents flowing at a node (junction) of a circuit is zero.
ΣI = 0 at node
This law follows directly from the conservation of electronic charge. The direction of each current flowing into or out of the node determines its sign.
Kirchoff’s 2nd Rule (Voltage Law)
This states that the sum of voltages around a closed loop is zero; ΣV = 0 in a loop.
This law is based on the conservation of energy - a charge traveling around the loop gains as much energy as it loses.
We know that the sum of voltage in a closed loop is equal to the sum of PD drops, so…
Σ(emfs - IRproducts) =0
“The algebraic sum of the products of the resistances of the conductors and the currents in them in a closed loop is equal to the total emf available in that loop.’
How do you do nodal analysis?
- In nodal analysis, you first choose one node as V = 0.
- Then you determine the potentials at the other nodes and label them, in this 2 and 4, in between the resistor and voltage source pair.
- The only unkown potential is the top node which is labelled as V1 . At that node we have three must have three current that sum to 0 because of kirchoffs 1st law. We can work out these currents individually
When do you use supernodes and how?
You use supernodes when the potential at both ends of a battery are unkown. As you can see you place a node behind the battery, calculate its voltage, which would be the negative of the the battery voltage. You then calculate the voltage difference between this node and V1 and plug it back into the eq.
What is the superposition theorem?
Superposition Theorem. The total current in any part of a linear circuit equals the algebraic sum of the currents produced by each source separately.
State Thevenin’s Theorem
Any linear network of voltage and current sources and resistors can be replaced by an equivalent circuit consisting of a single voltage source Vth in series with a single resistor Rth .
Vth is the voltage obtained at the output terminals of the real source when the output is open circuit. Rth is the resistance you would measure across the output terminals of the real source if all the emfs inside the source were short-circuited and all the current sources inside the source were open circuited.
What way does the voltage arrow point with respect to the direction of current?
Outside the source, it drops against the current.
What is Thevenin’s theorem only really good for?
Only designed for figuring out the current and voltage for the load.
