If sum of resistance is A and equivalent resistance in parallel combination is B , find the value of individual resistances.
Answers
Answer:
In the previous tutorials we have learnt how to connect individual resistors together to form either a Series Resistor Network or a Parallel Resistor Network and we used Ohms Law to find the various currents flowing in and voltages across each resistor combination.
But what if we want to connect various resistors together in “BOTH” parallel and series combinations within the same circuit to produce more complex resistive networks, how do we calculate the combined or total circuit resistance, currents and voltages for these resistive combinations.
Resistor circuits that combine series and parallel resistors networks together are generally known as Resistor Combination or mixed resistor circuits. The method of calculating the circuits equivalent resistance is the same as that for any individual series or parallel circuit and hopefully we now know that resistors in series carry exactly the same current and that resistors in parallel have exactly the same voltage across them.
For example, in the following circuit calculate the total current ( IT ) taken from the 12v supply.
resistors in series and parallel combination
At first glance this may seem a difficult task, but if we look a little closer we can see that the two resistors, R2 and R3 are actually both connected together in a “SERIES” combination so we can add them together to produce an equivalent resistance the same as we did in the series resistor tutorial. The resultant resistance for this combination would therefore be:
R2 + R3 = 8Ω + 4Ω = 12Ω
So we can replace both resistor R2 and R3 above with a single resistor of resistance value 12Ω
resistor combination circuit
So our circuit now has a single resistor RA in “PARALLEL” with the resistor R4. Using our resistors in parallel equation we can reduce this parallel combination to a single equivalent resistor value of R(combination) using the formula for two parallel connected resistors as follows.
combination resistive circuit
The resultant resistive circuit now looks something like this:
final resistor circuit
We can see that the two remaining resistances, R1 and R(comb) are connected together in a “SERIES” combination and again they can be added together (resistors in series) so that the total circuit resistance between points A and B is therefore given as:
R(ab) = Rcomb + R1 = 6Ω + 6Ω = 12Ω
equivalent resistance
Thus a single resistor of just 12Ω can be used to replace the original four resistors connected together in the original circuit above.
By using Ohm’s Law, the value of the current ( I ) flowing around the circuit is calculated as:
total circuit current
Then we can see that any complicated