Find The Equivalent Resistance Between Points A And B In The Drawing

Calculate the equivalent resistance between the points A and B for the following combination of resistors,

$Let comma space the space 4 space straight capital omega space resistors space be space connected space in space series. space straight R subscript 1 space equals space 4 space plus space 4 space plus space 4 space equals space 12 space straight capital omega Now comma space 2 space straight capital omega space resistors space are space also space connected space in space series. space straight R subscript 2 space equals space 2 plus 2 plus 2 equals 6 space straight capital omega Now comma space straight R subscript 1 space equals space 12 space straight capital omega comma space straight R subscript 2 space end subscript equals space 6 space straight capital omega space and space 4 space straight capital omega space are space connected space in space parallel. Therefore comma 1 over straight R subscript 3 equals 1 over 12 plus 1 fourth plus 1 over 6 equals fraction numerator 1 plus 3 plus 2 over denominator 12 end fraction equals 6 over 12 equals 1 half rightwards double arrow R subscript 3 equals 2 capital omega$

So, resistance between A and B, R = 5+2+6 = 13 , which is the required equivalent resistance.

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Three resistors are connected to a 6 V battery as shown in the figure given below:

Calculate:

i) the equivalent resistance of the circuit.

ii) total current in the circuit.

iii) potential difference across the 7.2 ohm resistor

Reistors 8 ohm and 12 ohm are in parallel.

Then, equivalent resistance is,

$Error converting from MathML to accessible text.$

Five resistors of different resistances connected together as shown in the figure. A 12 V battery is connected in the arrangement.

Calculate:

i) the total resistance in the circuit.

ii) the total current flowing in the circuit.

Here R₁ and R₂ are connected in parallel.

$1 over straight R equals 1 over R subscript 1 plus 1 over R subscript 2 space space space space space equals 1 over 10 plus 1 over 40 space space space space space equals 5 over 40 equals 1 over 8 rightwards double arrow space space space space space space R equals 8 capital omega$

And R₃, R₄ and R₅ are in parallel.

That is,

$1 over straight R to the power of apostrophe equals 1 over R subscript 3 plus 1 over R subscript 4 plus 1 over R subscript 5 space space space space space equals 1 over 30 plus 1 over 20 plus 1 over 60 space space space space space equals fraction numerator 2 plus 3 plus 1 over denominator 60 end fraction space space space space space space equals 1 over 10 space rightwards double arrow R apostrophe equals 10 capital omega$

i)Total resistance = R + R' = 8 +10 = 18 ohm

ii) Total current = =0.67 A

Two resistors of 4 ohm and 6 ohm are connected in parallel to a cell to draw 0.5 A current from the cell.

i) Draw a labeled circuit diagram showing the above arrangement.

ii) Calculate the current in each resistor.

i) The labeled circuit diagram is shown as below:

ii)
$Error converting from MathML to accessible text.$

The figure shows a new circuit. [Page 589]

When the circuit is switched on the ammeter reads 0.5 A.

i) Calculate the value of the unknown resistor R.

ii) Calculate the charge passing through the 3 ohm resistor in 120 s

iii) Calculate the power dissipated in the 3 ohm resistor.

i)
$Error converting from MathML to accessible text.$

ii)
$We space know space that comma space space straight q space equals it space equals space 0.5 space cross times space 120 space space space space space space space space space space equals space 60 space Coulomb$
iii)
Power, P = V.I.

= I²R

= (0.5)²x 3

= 0.25 x 3

P = 0.75 Watt

Three resistors are connected to a 12 V battery as shown in the figure given below:

i) What is the current through the 8 ohm resistor?
ii) What is the potential difference across the parallel combination of 6 ohm and 12 ohm resistor?
iii) What is the current through the 6 ohm resistor?

Here, 12 ohm and 6 ohm resistors are connected in parallel.

Therefore, their effective resistance, $fraction numerator 12 cross times 6 over denominator 12 plus 6 space end fraction space equals space 72 over 18 equals 4 straight capital omega$
Total resistance of the circuit = 8+4 = 12

i) Current drawn = $E over R equals 12 over 12 equals 1 space A$
That is, current through the 8 om resistor = 1 A

ii) P.D. across the 8 ohm resistor = I R = 1 = 8 V

P.D. across the parallel combination of resistors = 12 – 8 = 4 V

Because, the resistances are in parallel and they have the same P.D. each.

That is equal to 4 V.

iii) Current through the 6 ohm resistor = $Error converting from MathML to accessible text.$

Find The Equivalent Resistance Between Points A And B In The Drawing

Source: https://www.zigya.com/study/book?class=10&board=icse&subject=Physics&book=Concise+Physics+Part+II&chapter=Current+Electricity&q_type=&q_topic=Combination+Of+Resistors+&q_category=&question_id=IPHEN10107543

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