# Series Circuit

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#### What is DC Series Circuit?

When all the resistive components of a DC circuit are connected end to end to form a single path for flowing current, then the circuit is referred as series DC circuit. The manner of connecting components end to end is known as series connection.
Suppose we have n number of resistors $R_1$, $R_2$, $R_3$ . . . $R_n$ and they are connected in end to end manner, means they are series connected. If this series combination is connected across a voltage source, the current starts flowing through that single path. As the resistors are connected in end to end manner, the current first enters in to $R_1$, then this same current comes in $R_2$, then $R_3$ and at last it reaches $R_n$ from which the current enters into the negative terminals of the voltage source.
Fig. 1: Three resisters in DC series circuit.
In this way, the same current circulates through every resistor connected in series. Hence, it can be concluded that in a series DC circuit, the same current flows through all parts of the electrical circuit. According to Ohm's law, the voltage drop across a resistor is the product of its electrical resistance and the current flow through it. Here, current through every resistor is the same, hence the voltage drop across each resistors proportional to its electrical resistance value.
If the resistances of the resistors are not equal then the voltage drop across them would also not be equal. Thus, every resistor has its individual voltage drop in a series DC circuit.
The Fig. 2 shows only three resisters $R_1$, $R_2$ and $R_3$ in series with a DC voltage source V and the same Current I flowing through each resister. Voltage drops are $V_1$ in $R_1$, $V_2$ in $R_2$ and $V_3$ in $R_3$. According to ohm's law:
$$V1 = I \times R_1$$
$$V2 = I \times R_2$$
$$V3 = I \times R_3$$
From Fig.no.2 we can also conclude that the sum of all the voltage drops $V_1$, $V_2$, and $V_3$ are equal to the source DC voltage V. Hence given as;
$$\bbox[5px,border:1px solid red] {\color{blue}{V=V_1 + V_2 + V_3}}$$
$$\begin{array} {rcl} V &=& V_1 + V_2 + V_3 \\ V & = & I\times R_1+I \times R_2+I \times R_3 \\ V &=& I (R_1 + R_2 +R_3) \\ V &=& I \times R_T \end{array}$$
where $R_T$ is the Total Resistance of the three resisters in series circuit shown in [Fig. 1] equal to:
$$\bbox[5px,border:1px solid red] {\color{blue}{R_T = R_1+R_2+R_3}}$$
For Dc series Circuit:
• The manner in which the supply is connected determines the direction of the resulting conventional current.
• The current is the same at every point in a series circuit.
• The polarity of the voltage across a resistor is determined by the direction of the current.
• The applied voltage is the sum of all the voltage drops.
• The circuit can be reduced to one Total Resistor which is the sum of all the resisters in series.
• The difference of voltage drop value depends upon the value of resistors.
• If one of the resistor cuts off, current flow would stop in the circuit.
Example 1: For the series circuit in Fig. 2:
a. Find the total resistance $R_T$.
b. Calculate the resulting source current $I$.
c. Determine the voltage across each resistor.
Fig. 2: Series circuit to be analyzed in the example 1.

Solution: a: $R_T = R_1 + R_2 +R_3$
$$R_T = 2+3+5 = 10Ω$$
b: $E = I \times R_T$
$$I = {E \over R_T} ={10 \over 10} = 1A$$
c: $V_1 = IR_1 = (1)(2) = 2 V$
$$V_2 = IR_2 = (1)(3) = 3 V$$
$$V_3 = IR_3 = (1)(5) = 5 V$$

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