How to Find Voltage Across Resistor:Several Approaches And Problems Example


This article discussed how to find voltage across resistor in an effortless way, such as in series combination, parallel combination and other circuit combinations.

Voltage Across any resistor can be determined by:

  • Different circuit laws or rules such as Kirchhoff’s law, current division or voltage division rule.
  • Equivalent resistance of the required part of a circuitry.
  • By determining the characteristics or functions of the overall or part of the circuit.

How to find voltage across resistor in series ?

A series resistor circuit has only one path or branch for circuit currents to flow through. All resistors are connected to a single path or branch of the circuitry in this circuit type connection.

The voltage drop across any series combination of resistance may vary with the overall or individual resistor value.

Assuming there is more than one resistor connected to the series combination, then the whole combination of resistance can be replaced by a single resistor of equivalent resistance. Suppose the resistor in a series circuit is of identical values. In that case, the voltage drop (or electric potential drop) across each resistor can be identified as the current flowing through each resistor in the circuit is the same.

The overall voltage drop in any series resistor circuit equals the summation of voltage or potential drop across every individual resistor of the series circuit combination.

In which type of resistor circuit combination, the overall circuit voltage is divided between different resistors of the series circuit combination. The magnitude voltage across each resistor depends upon the value of resistance of the respective resistor to find the magnitude of current flowing through the resistor. 

Assume there are several resistors connected in a series circuit and [latex] V_1, V_2, V_3 … V_n [/latex] is the individual voltage drop across each resistor in a series circuit combination, then the total voltage drop across the series circuit can be denotated can be defined as

[latex] V =V_1 +V_2 +V_3 . . . +V_n [/latex]

To determine the total or overall equivalent resistance of a series circuit combination of ‘n’ number of resistors, make use of the formula:

[latex] R_e = R_1+ R_2 + R_3……+R_n [/latex]

Where [latex] R_e [/latex] is the equivalent or overall resistance of the series resistance combination

[latex] R_1, R_2, R_3. . . . .R_n [/latex] the resistance of individual resistors connected to the series circuit of ‘n’ numbers of resistors.

How to find voltage across resistor in parallel ?

Any circuit can be formed with series or parallel a combination of both series and parallel circuit design. 

The voltage drop (or electric potential drop) across the resistor in parallel can be determined or calculated easily by considering the characteristic of a parallel resistance circuit, as the voltage drop or electric potential drop across each path or branch in parallel combination is identical.

File:Resistors in parallel.svg
Image Credit: Resistances are in parallel combination. OmegatronResistors in parallelCC BY-SA 3.0

The current flowing through each branch in parallel circuit combination can be decided by the all-over resistance across the path or branch of the circuit. The overall current in a circuit equals the summation of instantaneous current through to an individual branch in a parallel circuit combination. If more than one resistor is linked to a parallel circuit, then those resistors can be replaced by only one resistor of equivalent magnitude.

A circuit is called a resistor’s parallel circuit combination, when more than one resistance is linking two circuit node’s, providing several paths for current to flow through.

Current through to every resistance can also be determined by current divider rule as the current throughout the circuit gets split up into all the branches in any parallel circuit of the resistor. The overall power dissipated in parallel combination is proportional to the summation of individual instantaneous power dissipated by any register in a parallel circuit combination.

As acknowledged, the overall voltage in resistance’s parallel circuit combination has the same magnitude as the electric potential drop across each path or branch of a resistance’s parallel circuit is constant.

Let’s assume that if there are several branches in a parallel circuit combination of resistance, then [latex] V_1, V_2, V_3, V_n [/latex] are the individual voltage drop across the overall resistance of each branch in parallel combination.

 Then [latex] V_1 =V_2 = V_3 . . .= V_n [/latex]

For example, suppose more than one resistor is connected in a parallel combination. The resistance values can be identical or different in any parallel circuit combination. Assume two resistors of identical resistance are linked in parallel combination with each other. In that case, the currents flowing through them will be the same in magnitude and with equivalent resistance and current division rule. After applying Ohm’s law, we can get the voltage across each resistance parallel. 

Assume that two resistors, [latex] R_1 [/latex] and [latex] R_2 [/latex], are of different resistances connected in parallel combinations. The current flowing through each resistance can be indifferent from each other.

After calculating the current through each branch by the current division rule and finding the value of equivalent resistance of an overall circuit can be calculated with Ohm’s law, the voltage across each resistance can be determined.

Equation of equivalent resistance in parallel combination with resistor:

[latex] \frac{1}{R_e}= \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} ……. +\frac{1}{R_n}[/latex]

Where [latex] R_e [/latex] -> Equivalent resistance of the parallel circuit combination.

[latex]R_1, R_2, R_3….R_n [/latex] -> Different resistor connected in parallel combination. 

When two resistors (R) in parallel are of the identical value, the equivalent resistance of both resistors is half of the one resistor (R).

As [latex] frac{1}{R_e}= \frac{1}{R} + \frac{1}{R} => \frac{1}{R_e} = \frac{2}{R} => R_e = \frac{R}{2}. [/latex]

How to find voltage across resistor in RL circuit?

RL circuit contains at least one resistor and inductor in the circuitry in parallel or series combination.

The voltage drop across the resistor in the RL circuit can be obtained (or determined) by applying Kirchhoff’s law. A first-order differential equation is generated, consisting of the voltage drop across the inductor and resistor. 

how to find voltage across resistor
Image Credit: Ea91b3ddSeries-RLCC BY-SA 3.0

For any RL circuit, the voltage drop across the resistor can be determined by current flowing through it along with the known value of the resistor with the help of Ohm’s law.

For the Series RL circuit,

[latex] V_r (s)= \frac{R}{R + Ls } Vin (s) [/latex]

For the parallel RL circuit,

[latex] I_r (s) = \frac{V_{in}}{R} [/latex]

How to find maximum voltage across a resistor?

Every resistor has a maximum power rating, which means that it is the maximum power that can be given to the specific resistor without damaging it.

From the current power relationship ([latex]P = I^2 R [/latex], where R is considered constant in this case) and by providing maximum power to the resistor while considering the maximum power rating of that specific resistor, maximum voltage across the resistor can be measured.

How to find voltage across a resistor in combination circuit?

A combination circuit is a combination or mixture of both series and parallel circuits together.

File:Combo3.png
Image Credit: DrjenncashCombo3CC0 1.0
  • Analysis of combination circuit is possible by breaking the possible parallel and series circuit combination.
  • And after breaking down the whole combination in different parts, analysis or equivalent of that specific parts can be calculated separately.
  • Then the total equivalent of the whole circuit combination can be calculated, after combining equivalent all parts (which was calculated separately).
  • By applying Ohm’s Law, Kirchhoff’s law, the voltage drop across any component in the circuit can be determined.

How to find RMS voltage across a resistor?

RMS voltage means root mean square voltage of an AC circuit, where RMS value denotes the equivalent power dissipation of a DC circuit.

In an AC circuit, the RMS voltage can be calculated from an AC circuit’s peak to peak voltage. Ohm’s Law, Kirchhoff’s Law, and other circuit laws can be applied to the AC circuit to calculate instantaneous voltage or current through the resistor.

Let [latex] V_r[/latex] be the instantaneous voltage across a resistor then [latex]V_r = V_p sin \omega t [/latex]

And [latex] I_r [/latex] be the instantaneous current through a resistor then [latex]I_r = \frac {V_r}{R} =Vmax/R sin \omega t = I_p sin \omega t [/latex]

So the voltage across a resistor can be defined as [latex] V_r = I_p R sin \omega t [/latex]

And [latex] V_{rms} = \frac{V_p}{\sqrt{2}} [/latex]

How to find voltage across load resistor?

The load resistor is a passive circuit element with two terminals that have some resistance value.

The voltage drop across the load resistance can be determined by determining the circuit combination and applying required circuit laws such as Ohm’s law, Kirchhoff’s law, etc. If required, then an equivalent circuit can be driven by simple calculations.

Sneha Panda

I have graduated in Applied Electronics and Instrumentation Engineering. I'm a curious-minded person. I have an interest and expertise in subjects like Transducer, Industrial Instrumentation, Electronics, etc. I love to learn about scientific researches and inventions, and I believe that my knowledge in this field will contribute to my future endeavors. LinkedIn ID- https://www.linkedin.com/in/sneha-panda-aa2403209/

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