Ohms Law and Voltage through Resistor. Simple Design 2


In a circuit diagram, we can see a number of Resistors connected in series or parallel between the positive and negative rails. These resistors are controlling the voltage and current to the particular sections of the circuit. When we design a circuit, we should have an idea about the voltage and current requirements for each section of the circuit. Then only we can select the proper values of resistors. If you know this, you can easily answer the questions in Project Viva regarding the selection of resistors.

First understand the Series and Parallel resistors. Series resistors means two or more resistors connected in series. This mainly appears as potential dividers in comparators, transistor amplifiers, oscillators etc. Parallel resistors mean two or more resistors connected parallel between the positive and negative rails.

Voltage across the Series resistor chain

See image. Two resistors R1 and R2 are connected in series across the 12 volt supply. So the total resistance is
R1 + R2 = 10,000 Ohms ( 10K) + 1000 Ohms ( 1K) = 11,000 Ohms
The relationship between Current, Resistance and Voltage as per Ohms law is Current I = V / R , IR = V, V = IR
Where I is the current in Amperes, V is the input voltage and R is the resistance in Ohms.
Now use basic algebra to change Ohms law to solve for voltage instead of Current.
I = V/R , IR = VR / R , IR = V, V= IR
So current I through R1 + R2 is = V/R = 12 V / 11, 000 Ohms
= 0.001,090,91 Amps
Voltage Drop across R1 and R2
We know Current and Resistance.
Current is 0.001,090,91 Amps
Resistance is 11, 000 Ohms
So Voltage V = I x R
Voltage drop across R1= V1 = 0.001,090,91 Amps x 1,000 Ohms ( 10K) = 10. 9091 V
Voltage drop across R2 = V2 = = 0.001,090,91 Amps x 1000 Ohms ( 1K) = 1.09091
So total voltage drop V1+V2 across R1 and R2 is
10.9091 + 1.09091 = 12 Volts. That is equal to the input voltage

That means, 10 K resistor allows 1,09091 volts and 1K resistor allows 10.9091 volts to pass.

See below images. The theory above explained exactly matches with the real situation.
Voltage across Parallel Resistors
See image. Here two resistors ( 10K and 1 K ) are connected in parallel across a 12 volt power supply.
So total voltage is V1 + V2
The total voltage through the resistor remains same as the entire circuit irrespective of the value of the resistors in parallel.
Total current through the resistors
Total current will be the sum total of the current running through each parallel path.
I total = I1 + I2
Here the resistors are 10,000 Ohms (10K) and 1000 Ohms (1K) and input voltage is 12 volts.
So 1 / R total
That is 1/10,000 + 1/ 1000 = 0.0001 + 0.001 = 0.0011
So R total is 1 / 0.0011 = 909.090,909 Ohms
Now Voltage across a Resistor
V = I x R
Input voltage (V)12 Volts
Current (I) = V / R = 12 V / 909.090,909 Ohms = 0.0132 Amps
So Voltage (V) across the resistors is I x R
That is 0.0132 A x 909.090,909 Ohms = 12 V