Solutions of the Parallel Circuits Questions

Finding of the equivalent resistance and the total current. Finding the voltage across any resistor that connected in parallel. Solutions of the questions about parallel connected circuits.


Solution 1

There are three of resistors connected in parallel in the circuit.

1 
= 1
+ 1
+ 1
R3
R2
R1
Rs





1 
1
+1
+1
6
3
6
Rs




1 
= 4
6
Rs




Rs = 6
4




Rs = 1.5 Ω


The right answer is option C.


Solution 2

There are three of resistors connected in parallel in the circuit.

1 
= 1
+1
+1
16
6
12
Rs




Rs = 48
15




Rs = 3.2 Ω


The right answer is option B.


Solution 3

The equivalent resistance of the resistors connected in parallel is founds as following.

1 
= 1
+1 +...
R2
R1
Rs





If Rs = 2 Ω

1 
=1
+1 
+1
8
R2 
8
2




1 
=R2 
+8
+R2
8R2
8R2
8R2
2





1 
= 2R2 + 8
8R2
2




8R2 = 4R2 + 16

4R2 = 16

R2 = 4 Ω


The right answer is option D.


Solution 4

If we find the value of resistor R2, we can find its current.

The value of the resistor R2,

1 
= 1
+1
R2
12
Rs




1 
= 1 
+ 1
R2
12
3





1 
= R2 + 12
12R2
3




12R2 = 3R2 + 36

9R2 = 36

R2 = 4 Ω

The total current of the circuit.

Is = V
Rs



Is = 36
3



Is = 12 A


The current flow through resistor R2.

IR2 = Is•R1
R1 + R2




IR2 = 12•12
16




IR2 = 9 A

The right answer is option C.


Solution 5 

The circuit have four of resistor connected in parallel.


1
1
+1
+1
+1
3
10
15
6
Rs




1
= 20
30
Rs




Rs = 1,5 Ω

The right answer is option D.


Solution 6

The voltage across the resistor R2 will be 60 V whatever the value of the resistor R2.

The current flow through in resistor R2 is founds with equality of 

IR2 = V
R2




For IR2 = 5 A,

5 = 60
R2




R2 = 12 Ω


The right answer is option A.


Solution 7

If there are n resistor and the value of these resistors are equal, the equivalent resistance of the circuit can found as following.

Rs =R
n




The R value in this formula is value of any resistor.

For R = 108, n = 12,

Rs =108
12




Rs = 9 Ω

In this case, the total current that drawn from supply source.

Is =72
9



Is = 8 A


The right answer is option B.


Solution 8

The total current of a circuit is founds as below.

Is =V
Rs




If the current drawn from supply source is 16 A and the supply voltage is 48 V.

Rs = 48
16




Rs = 3 Ω 

1 
=1
+1
+1
R3
8
12
3





1 
= 2R3
+3R3
+24
24R3
24R3
24R3
3




1 
=5R3 + 24
24R3
3




24R3 = 15R3 + 72

9R3 = 72

R3 = 8 Ω


The right answer is option B.


Solution 9

1 
= 1
+1
+1
R3
10
10
4




1 
= 2R3 + 10
10R3
4




10R3 = 8R3 + 40

2R3 = 40

R3 = 20 Ω

The right answer is option D.


Solution 10

The equivalent resistance of the resistors in order for can draw current of 10 A from the circuit must be

Rs = 60  = 6 Ω
10



The values of the resistor R2 and R3. The equivalent resistance of these resistors is

R2,3 = 60 = 30Ω
2




The value of the equivalent resistance of R1 and R2,3 is 

R1,2,3 = 30 =15 Ω
2




If a resistor R4 is connect to the circuit, the equivalent resistance must be 6 Ohm.

1 
= 1 
+1
R4
15
6




1 
= R4 
+15
15R4
15R4
6




1 
= R4 + 15
R4
6




15R4 = 6R4 + 90

9R4 = 90

R4 = 10 Ω

The value of the resistor which must be connect to the circuit is 10 Ω.


The right answer is option C


The questions

Series Connected Resistor Questions

Parallel Circuits Subject Expression



RISE KNOWLEDGE

28/10/2018

  • WRITE COMMENT
  • NAME SURNAME(or nick)
  • COMMENT
COPYRIGHT© ALL RIGHTS RESERVED