Formulas-Landscape Layout 2

1 Positive Voltages In some DC circuits, one point in the circuit is designated as the common-ground reference point and all voltages are measured relative to that point. Common-groundreferencepoint Points A, B, and C, are all positive relative to the reference point. Internal Resistance All voltage sources have some internal resistance such as the conductors in the coils of a generator or the chemicals in a battery. Internal resistance Ideal voltage source Battery Load The internal resistance of a voltage source can be represented as a resistance in series with an ideal voltage source. Normally this resistance is very small compared to that of the load and has little effect on circuit operation. When the internal resistance becomes a significant part of the total circuit resistance, we must take it into account. Determining Resistance There are various ways to find the total resistance of parallel resistances when the individual resistance values are known. For any parallel circuit the reciprocal equation can be used. R T = R 1 x R 2 R 1 + R 2 If the parallel circuit has only two branches, a more simple equation called the product over sum equation can be used. R T = R X Rn For parallel circuits with resistors of equal value, the value of one of the resistors is divided by the number of resistances. Solving DC Parallel Circuits The procedure for solving parallel-circuit values of voltage, current, resistance, and power is similar to that used for solving values for series circuits. The parallel-circ uit characteristic s of voltage, current, resistance, and power. I T = I 1 + I 2 + I 3 . . E T = E 1 = E 2 = E 3 . . . P T = P 1 + P 2 + P 3 . . . Ohm’s law as it applies to the circuit as a whole and to individual loads, as well, is used. I = E /R E = I x R R = E/ I Kirchhoff’s Laws Kirchhoff’s laws are an extension of Ohm’s law. They can be considered as additional tools for solving values for electric circuits. Used along with Ohm’s law, these laws allow you to analyze DC series-parallel circuit networks. R 1 R 2 R 3 R 4 R 5 R 6 R 7 ET Determining Resistance General procedures to be followed in reducing series-parallel networks: Reduce only one part at a time. After each circuit reduction redraw the circuit and exchange the equivalent resistor for the original resistors. Be sure that all series resistors have been combined before a parallel portion is reduced. Combine parallel portions to a single resistor. Repeat combining equivalent resistors until the circuit is reduced to one equivalent total resistance. Determining Power The total power supplied to a DC resistive circuit, whether series, parallel, or a combination, is equal to the sum of the power dissipated by the individual load resistors. P T = P 1 + P 2 + P 3 + ... + P n , (where n is the number of resistive components in the circuit) Therefore, each circuit component contributes to the total power dissipated by a DC series-parallel circuit. Voltage Source Internal Resistance When the internal resistance of a voltage source becomes a significant part of the total circuit resistance, you must take it into account when analyzing the circuit. Constant Current Source with Internal Resistance Current source Using the current divider rule (for a parallel circuit), the output current (or load current) can be determined in terms of R S and R L : The current source internal resistance R S is in parallel with the current source. R L = I S x R S R L + R S In reality, every current source has a parallel internal resistance(R S), which causes some loss of current. Converting Voltage and Current Sources Any voltage source with its series resistance can be converted to an equivalent current source with the same value of resistance in parallel. Divide the source voltage ES by its series resistance R S to calculate the current IS for the equivalent current source of the same value. To convert a current source to an equivalent voltage source, the source current IS is multiplied by its parallel resistance R S, to calculate voltage ES. Superposition Theorem The superposition theoremtreats each source as an independent source in the network, and then combines the individual results. The superposition theorem states the following: In a resistor network with two or more sources, the current through or the voltage across any component is the algebraic sum of the effects due to each independent source. Superposition Theorem In order to zero a current source, we replace it with an open circuit, since the current through an open circuit is zero amperes. Original current source (OPEN) Current source replaced with an open circuit Superposition Theorem The following steps are used applying the superposition theorem: 1. Zero all voltage or current sources but one. 2. Determine the current or voltage you need, along with its correct direction or polarity, just as if there were only one source in the circuit. Superposition Theorem 3. Repeat steps 1 and 2 for all the remaining sources in the circuit. Superposition Theorem 4.To find a specific current or voltage, algebraica lly combine the currents or voltages due to the individual sources. If the currents act in the same direction or the voltages are of the same polarity, add them. If they act in opposite directions, subtract them with the direction of the resultant current or voltage being the same as the larger of the original quantity. Thevenin's Theorem Thevenin's theorem is particularly useful in situations where the circuit is complicated, but the interest is in the current through or the voltage across a particular resistor, which is generally referred to as the load resistor or R L .

Formulas-Landscape Layout 2

Documents