# D.C. Circuits

1.6.1 Conservation of Charge and Kirchho ‘s 1st Law
Kirchhoff’s 1st Law conserves charge and states that the sum of the current owing into a point in a circuit is equal to the sum of the current owing out of that point.
1.6.2 Conservation of Energy and Kirchho ‘s 2nd Law
Kirchhoff’s 2nd Law conserves energy and states that the sum of the E.M.F.s is equal to the sum of the p.d.s in a loop in a circuit.
1.6.3 Voltage in Parallel circuits
In a parallel circuit, the voltage across the branches are equal.
1.6.4 Resistance in Series and Parallel circuits

1.6.5 * Resistance and Meters
An ammeter is in series and therefore for it to a ect the circuit the least, it’s resistance should be as close as possible to zero. A voltmeter is in parallel and so the resistance should be as large as possible, which is why digital voltmeters are so much more accurate the analogue ones, because they use much larger resistors and they a ect the results much less.

1.6.6 * Thermistors
Negative Temperature Co-e cient (NTC) thermistors are unusual in terms of resistance, since their resistance decreases with increased temperatures, this happens because the atoms vibrate more due to the increased temperature and more electrons are `unlocked’ which increases the n in nAve and so there is more current and less resistance for a xed voltage. You can remember this as Temperature Up Resistance Down (TURD).
1.6.7 Potential Dividers
A potential divider is used to split E.M.F. which is normally known as VIN. The potential is split using two resistors and VOUT is connected around on of the resistors and one of the resistors is varied which allows you change VOUT. The formula is derived as follows (where VOUT is over R2):

1.6.8 Electromotive force, Potential di erence and Voltage
Electromotive force and Potential di erence are the two types of voltage. An Electromotive force (E or E.M.F.), is when energy is gained per Coulomb between two points. A Potential di erence (p.d.), is when energy is lost per Coulomb between two points. E.M.F. is found in batteries/power supplies and a p.d. is found everywhere else (e.g. bulbs, resistors, etc.).

1.6.9 Internal Resistance
Power supplies are made of conductive materials which themselves have resistance, so contained in a power supply is some `internal resistance’. This resistance is often neglected because it has a very small value compared to the rest of the set up (usually ≈ 5Ω). To nd the internal resistance of any power supply, we must take that the given E.M.F. of the power supply, and since we know that V = IR, and that in a series circuit we add up branches to nd total p.d., we nd that E = IR +Ir, where I is the current read o of an ammeter in the circuit, R is the resistance of the components in the circuit, and r is the internal resistance. E = IR + Ir is sometimes written as E = V + Ir or V = E −Ir which is how it is shown on the formula booklet.