To find the value of an unknown resistor in series connections using ONLY a voltmeter isn’t that hard! however, it might seems to be but, this post will put you through the easiest step by steps to do that.

**Example of a problem like this:**

Consider two Resistors in series connection; one has 1KΩ resistance while the other is of unknown value. If the potential difference across the two resistors reads 9V, calculate the value of the unknown resistor. Also, find the total resistance to the flow of current in circuit?

In a situation where a problem of this nature occurs, a practical or an experimental idea is needful. Look carefully to the problem. If someone will use Ohm’s Law or resistors in series calculations ideas only to approach such problem, probably will hook somewhere along the way.

**Reasons **

- The current flowing through the circuit is unknown.
- The other value of the resistor is unknown thereby making calculation of the total resistance of the circuit a bit hard.
- “Using voltmeter ONLY to find unknown value of a resistor….” is not easy. Why? Because; Voltmeter as a measurement instrument only measures voltage or potential difference.
- Other challenge(s) you might figure out.

What then is the strategy to approach and solve such a problem? As we mentioned earlier, a practical or an experimental idea is needful.

Follow the step by steps below

**Step 1**

Set up the network in this form

**Step 2**

Measure the voltage drop across the given value resistor that is ** R_{1}** (from point A to B). Note the reading down as

**. For Example if your voltmeter read 5**

*V*_{1}*, then*

**V****= 5**

*V*_{1}

**V****Step 3**

Find ** V_{2}** either by measuring the voltage drop across the unknown value resistor

**(from point B to C) or, use the mathematics below.**

*R*_{2}Since ** V_{Total} = V_{1 }+ V_{2}**, Hence;

**9 = 5 + V_{2}**

Therefore; *V _{2} *= 9

_{ }– 5

*V _{2} *

**= 4**

*V**Note that V_{1} + V_{2} = V_{Total}*

**Step 4**

Due to the series connection of the resistors, the same current will flow through them. Therefore, let’s calculate the current using the known value resistor, (** R_{1}**=1KΩ). Note that converting 1KΩ to Ω gives 1000Ω (1 × 1000).

Using Ohm’s Law; *V = IR*

** V** across

**is given by**

*R*_{1}**(**

*V*_{1}= IR_{1}**is the same across**

*I***and**

*R*_{1}**).**

*R*_{2}Therefore the current through *R _{1}*

*V _{1} = IR_{1}*

Therefore; *I=V _{1}/R_{1}*

**5/1000**

** I **=

**0.005**(This is the current that will flow through the two resistors that is; the whole circuit).

*A***Step 5**

Find the value of the unknown resistor (** R_{2}**) using this formula

*V _{2} = IR_{2}*

Therefore; *R _{2} = V_{2}/I*

**4/0.005**

*R _{2} *

**= 8000**(This is value of the unknown resistor).

*Ω***Step 6**

The total resistance of the circuit is;

** R_{Total} = R_{1 }+ R_{2} **(see resistors in series calculations)

Hence;

**1000 + 800**

**=1800 Ω** or 1.8KΩ (this is therefore the total resistance of the circuit).

That’s it!

**READ ALSO THESE**

Resistors and Types of Resistors / Ohm’s Law and its Limitations / Determining unknown resistors values / How to measure unknown Resistor’s value using multimeter / Resistors in Series Calculations / Resistors in Parallel Calculations / How to read resistor colour codes