Question

If a 6V battery is connected to the arrangement of three resistors of
40, 60, 120, in parallel, calculate the total current flowing in the circuit.​

Answer 1

Answer :-

✳Total Current in the circuit

= 0.25 A

________________________________

★ Concept :-

Here the concept of Combination of Resistances in Parallel Combination is used. According to this, if two or more resistances are connected in parallel, then their net equivalent resistance, R(eq) is given by :-

$\large{\boxed{\boxed{\bf{R_{eq(p)} \: = \: \dfrac{1}{R_{1}} \: + \: \dfrac{1}{R_{2}} \: + \: \dfrac{1}{R_{n}}}}}}$

where, 'p' denotes parallel combination and 'eq' denotes equivalent resistance.

• Resistance, R = (Potential Difference, V) /(Current, I)

_______________________________

★ Solution :-

Given,

▶Arrangement of Resistors = Parallel

▶Potential Difference of the Battery, V

= 6 V

▶ Resistance of Resistor 1 , R(1) = 40 Ω

▶ Resistance of Resistor 2 , R(2) = 60 Ω

▶Resistance of Resistor 3, R(3) = 120 Ω

Let the current of the circuit be 'I' then,

_____________________

By ohm's Law, we get,

✒ Resistance = Voltage / Current

Since, Voltage = Potential Difference

Here, first we need to find the total resistance of the circuit. Henceforth it will be net equivalent resistance of the circuit.

For parallel combination, Net equivalent Resistance is given by :-

✏ 1/R(eq) = {1/R(1)} + {1/R(2)} + {1/R(3)} ...

By applying values, we get,

✏ 1/R(eq) = (1/40) + (1/60) + (1/120)

By taking the LCM of RHS, we get,

✏ 1/R(eq) = (3 + 2 + 1) / 120

✏ 1/R(eq) = 5/120

✏ 1/R(eq) = 1/24

By taking reciprocal of both sides, we get,

✏ R(eq) = 24 Ω

Hence net equivalent resistance of the circuit = 24 Ω

_______________________________

Now by applying the values in Ohm's Law, we get,

➡ Resistance = Voltage / Current

By cross multiplying, we get,

➡ Current = Voltage / Resistance

➡ I = V / R

➡ I = 6 / 24

➡ I = 1/4 = 0.25 A

✳HENCE, THE CURRENT THROUGH THE CIRCUIT = 0.25 A

_____________________

★ Aid to Memory :-

• Resistance is the opposition faced by electrons that are provided potential difference while travelling in a conductor. It is denoted by R and its unit is Ω (ohm).

• Current the flow of electrons from lower potential to hight potential is known as current. It is denoted by I and its unit is A(ampere).

• Potential Difference is the difference or work done between higher and lower potential that helps to move a unit + charge from infinity to another point. It is denoted by P.D. (Potential Difference) and its unit is V (Voltage).

• Ohm's Law is the law given by a scientist for conductors that follow this law as Resistance is directly proportional to Voltage and inversely proportional to current.

• Resistance in Series Combination is given by,

=> R(eq(s)) = R(1) + R(2) + R(3) + ......

Answer 2

Answer :-

✳Total Current in the circuit

0.25 A

________________________________

★ Concept :-

Here the concept of Combination of Resistances in Parallel Combination is used. According to this, if two or more resistances are connected in parallel, then their net equivalent resistance, R(eq) is given by :-

$\large{\boxed{\boxed{\bf{R_{eq(p)} \: = \: \dfrac{1}{R_{1}} \: + \: \dfrac{1}{R_{2}} \: + \: \dfrac{1}{R_{n}}}}}}$

where, 'p' denotes parallel combination and 'eq' denotes equivalent resistance.

• Resistance, R = (Potential Difference, V) /(Current, I)

_______________________________

★ Solution :-

Given,

▶Arrangement of Resistors = Parallel

▶Potential Difference of the Battery, V

= 6 V

▶ Resistance of Resistor 1 , R(1) = 40 Ω

▶ Resistance of Resistor 2 , R(2) = 60 Ω

▶Resistance of Resistor 3, R(3) = 120 Ω

Let the current of the circuit be 'I' then,

_____________________

By ohm's Law, we get,

✒ Resistance = Voltage / Current

Since, Voltage = Potential Difference

Here, first we need to find the total resistance of the circuit. Henceforth it will be net equivalent resistance of the circuit.

For parallel combination, Net equivalent Resistance is given by :-

✏ 1/R(eq) = {1/R(1)} + {1/R(2)} + {1/R(3)} ...

By applying values, we get,

✏ 1/R(eq) = (1/40) + (1/60) + (1/120)

By taking the LCM of RHS, we get,

✏ 1/R(eq) = (3 + 2 + 1) / 120

✏ 1/R(eq) = 5/120

✏ 1/R(eq) = 1/24

By taking reciprocal of both sides, we get,

✏ R(eq) = 24 Ω

Hence net equivalent resistance of the circuit = 24 Ω

_______________________________

➡ Resistance = Voltage / Current

Resistance = Voltage / CurrentBy cross multiplying, we get,

➡ Current = Voltage / Resistance

➡ I = V / R

➡ I = 6 / 24

➡ I = 1/4 = 0.25 A

✳HENCE, THE CURRENT THROUGH THE CIRCUIT = 0.25 A

_____________________

★ Aid to Memory :-

• Resistance is the opposition faced by electrons that are provided potential difference while travelling in a conductor. It is denoted by R and its unit is Ω (ohm).

• Current the flow of electrons from lower potential to hight potential is known as current. It is denoted by I and its unit is A(ampere).

• Potential Difference is the difference or work done between higher and lower potential that helps to move a unit + charge from infinity to another point. It is denoted by P.D. (Potential Difference) and its unit is V (Voltage).

• Ohm's Law is the law given by a scientist for conductors that follow this law as Resistance is directly proportional to Voltage and inversely proportional to current.

• Resistance in Series Combination is given by,

=> R(eq(s)) = R(1) + R(2) + R(3) + ....