Electronics - Parallel Circuits - Discussion

We know that if voltage increases, current increases & if resistor increase then current decreases.. then in parallel current ckt as increases total resistance also increases...

According to the parallel resistance circuit the equivalent resistance is given by RT=R1||R2= (R1*R2)/(R2+R2. That answer will be less compare with when any one resistance open, because the total resistance is equalto RT=R1 or R2 only. So RT is increases.

If we consider the two resistance in parallel, r1 &r2, So according law R1*R2/ (R1+R2). If one of them is open means R1=NO, So it will be R2 in Series. So total resistance will decrease.

As we know for a particular resistor in series net resistance is greater than a resistance in parallel if we remove resistor of one of them from a parallel circuit the net result will increases as reverse as in series.

Can you give me the proper explanation? I want correct answer.

In parallel resistance the effective resistance value will be less than the smallest valued resistance. For eg, if a 2 ohm and 3 ohm resistance are in parallel effective resistance will be less than 2 ohm. So when one is opened the effective resistance increases.

Case 1: R1&R2 in parallel

RT=(R1XR2)/(R1+R2)

Case 2 : R2 is open circuited

RT= R1

To understand correctly

case 1: R1=1k R2=1k

RT= (1x10^6)/(2x10^3)

RT= 0.5k

case 2: R1=1k

RT=1k

So RT increases with removal of R2

Consider two resistors in parallel. Their total resistance is,

(R1 * R2) / (R1 + R2)

We would like to determine the effect of opening R2. The circuit then contains a single resistor, R1 in series. We would then like to determine whether ? is > or < in the below equation,


(R1 * R2) / (R1 + R2) ? R1

Let's multiply both sides of this inequality by (R1 + R2), which yields,

R1 * R2 ? R1 * (R1 + R2)

expanding the right hand side yields,

R1 * R2 ? R1^2 + R1 * R2

Since resistance is always positive, we have that the right hand side is larger. Therefore, we conclude that resistance will increase.

Let me explain with the example

Let
R1 = 4 & R2 =4
Then
RT = R1* R2/( R1+R2)
=4*4/4+4
=16/8
=2 ohms


If R1 is open then R1= not available
So RT = R2
=4

That means total resistance increases as one of the resistance is opened.

What will be answered if more than two resistance is connected in a circuit? Like, r1=2, r2=3, r3=4.