# Resistor Basics

## Resistors are Used For Lighting Up LEDs Smoothly

In order to light up a LED (light emitting diode), it is necessary to apply a voltage of about 2V across its two terminals. Therefore, the voltage is not enough to light up the LED with one single dry cell (about 1.5V) as shown in Fig. 1 (a). If instead, two dry cells are connected in series as shown in Fig. 1 (b), the voltage of about 3V will be too much and excessive current will flow through the LED thereby destroying the LED. If a suitable resistor is placed between the LED and the dry cells as shown in Fig. 1 (c), the LED lights up with an appropriate brightness without placing too much load either on the LED or on the batteries.

Thus, a resistor is one that causes electric circuits to operate smoothly by limiting the flow of current and is an essential component in any electric circuit.

(a) No light emission

(b) Too much current flows

(c) Ideal operating condition

## Recapture Ohm's Law

In the last example, it was mentioned that you need to use a resistor in order to operate an electric circuit, but let's take a closer look at how to determine the appropriate resistance value required in order to do so. This is given by the Ohm's law which states that the voltage(V) and the current(I) are related by the following equation:

…(1)

Here, R is the proportional constant of voltage(V) to current(I) and is called the electric resistance or simply resistance (unit: Ω). A resistor is simply this resistance realized as an electronic component.

## What is the Size of the Resistor in Fig. 1 (c)?

Let us now think of the meaning of Ohm's law. In the circuit of Fig. 2 above, if we assume that the voltage(V) is 1V and the current(I) is 1A, then according to the equation (1) above, the resistance(R) will be:

In other words, a 1(Ω) resistor is one through which a current of 1A flows when a voltage of 1V is applied across it. Or, the one which causes a voltage of 1V to appear across it when a current of 1A is passed through it. However, when the voltage remains the same at 1V but the current is 0.2A, the resistance value required is:

Also, the voltage required to pass a current of 1A through a 5(Ω); resistor is given by the following equation:

Thus, Ohm's law is always satisfied in an electric circuit, and hence if the values of any two of the voltage, current, and resistance are known, it is possible to determine the value of the remaining parameter.

Now, let's look at the value of the resistor required in the example of Fig. 1 (c). When the LED is operating normally, the voltage across its two terminals will be about 2V, and by subtracting the voltage of 2V across the two terminals of LED from the battery voltage of 3V, we get the voltage VR across the two terminals of the resistor as follows:

If we take the current ILED to be passed through the LED for normal operation as 15mA (1mA = 1/1000A), then the resistance(R) value required will be the following according to Ohm's law:

Therefore, the resistance value of the resistor in Fig. 1 (c) will be 67(Ω).

## Power Consumption and Rated Power

Energy is required for people to be able to work, even electrical equipment such as motors, heaters, lamps, etc., require energy to operate. The amount of energy required Power consumption and rated power is expressed by the parameter called power consumption. Since electric power (even this power consumption) is expressed as a product of the voltage and current, the power P is given by the following equation:

Since a voltage appears according to Ohm's law across the two terminals of a resistor when a current is passed through it, electric energy is consumed even in a resistor like electrical equipment. For example, when a current of 1(A) is passed through a resistor of 1(Ω), since a voltage of 1(V) appears across the resistor according to Ohm's law, the power consumption will be:

Thus the power consumption in the resistor is 1(W). In the case of a resistor, since this power will entirely be radiated as heat, if the power consumption is high, the temperature of the resistor itself increases, thereby finally burning it or melting it down. Therefore, it is necessary to indicate the amount of power the resistor can safely consume, and this power is called the rated power of the resistor. Normally, a resistor is used at a power consumption of less than 1/2 of the rated power so that we don't burn it out.

## Serial Connection and Parallel Connection

The connections in electric circuits can be classified broadly as serial connections and parallel connections which are shown in Fig. 3. When several resistors are connected together, the combined resistance value will be different in serial and parallel connections as follows:

In the case of serial connection:

In the case of parallel connection:

Consequently, the corresponding combined resistance values in Fig. 3 will be as follows:

(a) The combined resistance in the case of a serial connection is:

(b) The combined resistance in the case of a parallel connection is:

In other words, in the case of serial connection, the combined resistance value increases as the number of resistors in the connection becomes large and decreases in parallel connection as the number of resistors in the connection increases.

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