How to Solve Parallel Circuit Equations With Two Unknown Variables
Solving simple circuits with Kirchhoff's Laws and Ohm's Law can be challenging, but it's an essential skill for anyone interested in electronics. Most introductory physics classes in electricity and magnetism teach students how to analyze simple circuits. Tests in these classes often feature problems requiring you to find unknown values in a circuit from the values you already know.
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Instructions
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1
Determine what kinds of components are present in the circuit. Circuit diagrams use basic symbols to represent the various types of components. A light bulb is essentially the equivalent of a resistor for the purposes of this type of problem. Although in practice the resistance of a light bulb, or other metal element, increases with increasing temperature, introductory physics classes will ask you to treat light bulbs as simple resistors.
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2
Use the arrangement of the resistors, batteries or capacitors in the circuit to determine the net resistance, capacitance or voltage. When capacitors are in parallel, the total capacitance is the sum of the capacitances for all capacitors. When resistors are in parallel, the total resistance is the sum of the reciprocal of the resistance for each component, or 1 / total resistance = 1 / R1 + 1 / R2 + 1 / R3 and so on. When batteries are in parallel, their total voltage is equal to the voltage of either battery if it were alone. (It's unwise to link up two batteries of different voltages in parallel because a lot of current will flow from the higher voltage battery to the lower voltage one.)
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3
Use Ohm's Law (V = IR, where V is voltage, I is current and R is resistance) and Kirchhoff's Laws to set up two or more equations. Because you have two unknowns, you need at least two equations to solve for them. Kirchhoff's Laws state that the total voltage around a closed loop must be equal to 0. The laws also state the sum of the currents flowing out of a junction is equal to the sum of currents flowing into a junction. Given these facts, you can write equations for each of the current values in the parallel circuit.
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4
Determine which values you already have and which you need to find. If you are working a test or homework problem, some of the values will already be given to you. In general, you'll have two unknowns you need to calculate.
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5
Solve one of the equations in Step 3 for a variable that occurs in another equation then substitute. If you have an equation that only has one variable, you may be able to solve for that variable without substitution. This situation will probably only happen when you are working with simple circuits.
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