How to solve resistor in series problems

How to Solve resistor in series problems

Here in this article we will go through a easy problem showing the basics how to solve the problems where resistors are connected in series and you have to find the equivalent resistance of the circuit. we will do this through an example . For this consider studying the question given below and how I solve this question following several steps. Here our goal will be to analyze few resistors connected in series combination. Further If you want to read the notes related to this topic please follow this link

Question

A 10 V battery is connected to four resistances of resistances 2, 3, 4 and 6 $\Omega$ each and all the resistances are connected in series combination. Find the equivalent resistance for the circuit and current in the circuit.

Solution

Strategy

Since it is given in the question that the resistors are connected in series so summing their resistances gives the equivalent resistance. Here Ohm’s law can then be used to find the current.

1. First we should summarize the information given in the question. So as given in the question

Known Quantities : $\Delta V=10 V$

$R_{1}=2 \Omega$

$R_{2}=3 \Omega$

$R_{3}=4 \Omega$

$R_{4}=6 \Omega$

Unknown Quantities : $R_{eq}= ? $ and $I = ? $

Now we’ll draw the diagram which is given as follows

2. Now you will evaluate your situation I mean you need to choose the equations you have learned while studying the topic and decide which one would suite the best so that you gat the unknown quantities that are to be calculated.

So here in this case, we know that all four resistors are connected in series combination so the equivalent resistance can be calculated with the equation for resistors in series that is

$R_{eq}= R_{1}+R_{2}+R_{3}+……..$                                            (1)

Current in the circuit can be evaluated by using following equation

$\Delta V = IR_{eq}$                                (2)

3. Now that you have identified the equations you can now rearrange the equations to isolate the unknowns. Here in this case you can find $R_{eq}$ from equation (1) and rearrange equation (2) to find current in the circuit. So for current in the circuit our equation would look like

$I=\frac{\Delta V}{R_{eq}}$

4. We would now substitute the known values into required equations and then solve the equations.

So here,

$R_{eq}=2 \Omega +3 \Omega +4 \Omega +6 \Omega  $

or

$R_{eq} = 15 \Omega $

Now substitute the equivalent resistance value into the equation for calculating the current

$I = \frac {\Delta V}{R_{eq}}$

or,

$I= \frac{10}{15}=.67 A$

5.  Now that you have calculated the unknowns you can now evaluate the results. For example here for resistors connected in series , the equivalent resistance should be greater then the largest resistance in the circuit and here

$15 \Omega > 6 \Omega $