Circuits exist in everyday electronic devices such as computers and cell phones. Although circuits can be complex and include a myriad of components, such as resistors, inductors, capacitors and switches, each of these components will experience a voltage drop when in a circuit. A voltage drop is the amount the voltage lowers when going across an element, such as a resistor. In simple circuits where there is only a battery and a resistor, you might only need a little bit of common sense to determine the voltage drop. In more complicated circuits, you can calculate it using Ohm's Law, which states that, in a closed circuit, V=I*R; or, "voltage is equal to the current multiplied by the resistance."

## A Simple, Closed Circuit

Draw a simple circuit. To do this, draw the symbol (see link in Resources) for a battery on the left-hand side of the page. Label it V. Then, draw a symbol for a resistor approximately two inches to the right of the battery. Label it R. Finally, draw two solid lines. The first should connect the top of the battery symbol to the top of the resistor symbol and the second should connect the bottom of the battery symbol to the bottom of the resistor symbol.

Fill in values for the battery and the resistor: Next to the battery, write V = 10 Volts and R = 1 Ohm.

Equate the voltage of the power source to the voltage drop across the resistor.

According to Kirchhoff's Voltage Law, the voltage in a circuit must add up to 0 Volts. Or, put another way, the combination of each individual voltage drop must equal the voltage applied to the circuit. Therefore, since the battery in this simple circuit is applying 10 Volts, then the only other element in the circuit -- the resistor -- must experience a voltage drop of 10 Volts.

## Resistors in Series

Draw a circuit with two resistors in series. To do this, draw the symbol (see link in Resources) for a battery on the left-hand side of the page. Label it V. Draw a symbol for a resistor approximately two inches to the right of the battery and label it R1. Then, draw another resistor symbol half an inch before the first resistor. Label it R2. Finally, draw three solid lines. One line should connect the top of the battery symbol to the top of the resistor symbol labeled R1. The second should connect the bottom of the battery symbol to the bottom of the resistor symbol labeled R2. The final line should connect the bottom of R1 to the top of R2.

Fill in values for the battery and the resistors. Label the battery as V = 10 Ohms, label the first resistor as R1 = 2 Ohm and label the second resistor as R2 = 3 Ohm.

Add together the values of all the resistors, because when resistors are in series, you can simply think of them as one big resistor. It may be useful to redraw the circuit so it looks like a simple circuit with a battery source labeled V = 10 Volts and a single resistor labeled Rtotal, where Rtotal = 5 Ohms.

Use Ohm's Law to calculate the current for the circuit. First, rearrange the equation so that I = V/R. Then, replacing V with 10 Volts and R with the value of Rtotal, which is 5 Ohms, you can find the current. In this case, I = 2 Amps.

Note that, in a circuit where the resistors are in series, the current flowing each resistor will be the same value. This means that R1 and R2 will both have a current of 2 Amps flowing through them.

Re-examine your original drawing that has the two resistors, R1 and R2. Calculate the voltage drop across each individual resistor, using Ohm's Law in the form V = I_R, where I = 2 Amps. The voltage drop across R1 will be (2 Amps)_(2 Ohms), or 4 Volts. The voltage drop across R2 will be (2 Amps)*(3 Ohms), or 6 Volts.

Check that the voltage drop across the resistors is equivalent to the voltage from the battery to ensure that Kirchhoff's Voltage Law has been maintained. Since R1 has a voltage drop of 4 Volts and R2 has a voltage drop of 6 Volts, you can rest assured that you have calculated the voltage drops correctly because their combined voltage drop is equal to the voltage at the power source: 10 Volts.

## Resistors in Parallel

Draw a circuit with two resistors in parallel. To do this, draw the symbol (see link in Resources) for a battery on the left-hand side of the page. Label it V. Draw a symbol for a resistor approximately two inches to the right of the battery and label it R1. Then, draw another resistor symbol two inches to the right of the first resistor. Label it R2. Finally, draw four solid lines. One line will connect the top of the battery symbol to the top of the resistor symbol labeled R1. The second should connect the top of R1 to the top of the second resistor, labeled R2. The third should connect the bottom of the battery symbol to the bottom of R1 the resistor symbol labeled R2. The final line will connect the bottom of R1 to the bottom of R2.

Fill in values for the battery and the resistors. Label the battery as V = 10 Ohms, label the first resistor as R1 = 2 Ohm and label the second resistor as R2 = 5 Ohm.

Equate the voltage of the power source to the voltage drop across each resistor.

Since the positive terminals of the resistors are all connected together, and the same is true for the negative terminals, the voltage drop across each resistor will be equal to the voltage of the power source. Therefore, R1 will have a voltage drop of 10 Volts, and R2 will also have a voltage drop of 10 Volts.

#### Tip

Ohm's Law states that V=I*R, where V is voltage, I is current and R is resistance.

In a series circuit, the voltage drop across each resistor will be directly proportional to the size of the resistor.

In a parallel circuit, the voltage drop across each resistor will be the same as the power source. Ohm's Law is conserved because the value of the current flowing through each resistor is different.

In a series circuit, the total resistance in the circuit is equal to the sum of each resistor's resistance.

In a parallel circuit, the the reciprocal of the total resistance in the circuit is equal to the sum of the reciprocal value of each resistor's resistance, or 1/Rtotal = 1/R1 + 1/R2 + ... +1/Rn, where Rn is the number of resistors in the circuit.