Answer
Verified
376.5k+ views
Hint: The equation for the net resistance for two resistors of resistances connected in parallel hast to be used first.
Further, Ohm's law and Kirchoff’s current law will also be used to find the number of resistors.
Formula used:
The net resistance for two resistors of three resistances \[({R_1}),({R_2})\]and \[\left( {{R_3}} \right)\] connected in parallel will be in relation
$ \Rightarrow \dfrac{1}{R} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}}$
Ohm's law 🡪$V = IR = > I = \dfrac{V}{R}$
Kirchoff's current law 🡪$I = {I_1} + {I_2} + {I_3}$
Complete step-by-step solution:
Let's find out how a parallel resistance circuit works. A parallel resistance circuit is
made below.
The voltage source is $(V)$ and the net amount of current flowing through the circuit is $(I)$. There are three resistances \[({R_1}),({R_2})\] and \[\left( {{R_3}} \right)\]which are connected in parallel to each other. The amount of current passed through each branch of the resistor is given by: \[\left( {{I_1}} \right),\left( {{I_2}} \right)\]and \[\left( {{I_3}} \right).\]
The values of the individual amount of current through each resistance can be found through Ohm's law$V = IR = > I = \dfrac{V}{R}$
Hence, the value $({I_1})$is ${I_2} = \dfrac{V}{{{R_2}}}$and the value $({I_3})$is${I_3} = \dfrac{V}{{{R_3}}}$
Using Kirchoff's current law$I = {I_1} + {I_2} + {I_3}$
Hence,$I = {I_1} + {I_2} + {I_3}$ becomes
$I = {I_1} + {I_2} + {I_3}$
$ \Rightarrow \dfrac{V}{R} = \dfrac{V}{{{R_1}}} + \dfrac{V}{{{R_2}}} + \dfrac{V}{{{R_3}}}$
$ \Rightarrow \dfrac{1}{R} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}}$
Let's consider a special case of the resistances connected in parallel. In this case, the resistances are of the same value, that is $\dfrac{1}{{{R^/}}} = \dfrac{1}{R} + \dfrac{1}{R} + \dfrac{1}{R} = = > \dfrac{1}{{{R^/}}} = \dfrac{3}{R} = = > {R^/} = \dfrac{R}{3}$
Hence, the net resistance of the circuit becomes one-third the value of the resistance in each of the branches. Using the same formulation for $N$ branches, we get
${R_{net}} = \dfrac{R}{N}$-----🡪(1)
Where$(R)$is the resistance of each branch and $(N)$is the number of branches
For the current problem, we have multiple $176\Omega $ in parallel to each other. These
are connected to $220V$the line and the net current is $5A$ Hence using Ohm's law
and the value of resistance from the equation $(1)$, we get
$V = I{R_{net}} = = > 220 = 5(\dfrac{{176}}{N}) = = > N = (\dfrac{{176}}{{44}}) = = > N = 4$
Hence, 4 of the $176\Omega $resistors in parallel would be required to get a net current
of $5A$ flowing through a $220V$ line.
Note: It's important to remember that in a parallel resistance circuit connection, the voltage drawn by all the resistances is equal. An everyday example of this is the way electricity reaches all our houses. The constant $220V$ voltage is supplied to all the households in a locality since all the houses are in a parallel connection to each other.
Further, Ohm's law and Kirchoff’s current law will also be used to find the number of resistors.
Formula used:
The net resistance for two resistors of three resistances \[({R_1}),({R_2})\]and \[\left( {{R_3}} \right)\] connected in parallel will be in relation
$ \Rightarrow \dfrac{1}{R} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}}$
Ohm's law 🡪$V = IR = > I = \dfrac{V}{R}$
Kirchoff's current law 🡪$I = {I_1} + {I_2} + {I_3}$
Complete step-by-step solution:
Let's find out how a parallel resistance circuit works. A parallel resistance circuit is
made below.
The voltage source is $(V)$ and the net amount of current flowing through the circuit is $(I)$. There are three resistances \[({R_1}),({R_2})\] and \[\left( {{R_3}} \right)\]which are connected in parallel to each other. The amount of current passed through each branch of the resistor is given by: \[\left( {{I_1}} \right),\left( {{I_2}} \right)\]and \[\left( {{I_3}} \right).\]
The values of the individual amount of current through each resistance can be found through Ohm's law$V = IR = > I = \dfrac{V}{R}$
Hence, the value $({I_1})$is ${I_2} = \dfrac{V}{{{R_2}}}$and the value $({I_3})$is${I_3} = \dfrac{V}{{{R_3}}}$
Using Kirchoff's current law$I = {I_1} + {I_2} + {I_3}$
Hence,$I = {I_1} + {I_2} + {I_3}$ becomes
$I = {I_1} + {I_2} + {I_3}$
$ \Rightarrow \dfrac{V}{R} = \dfrac{V}{{{R_1}}} + \dfrac{V}{{{R_2}}} + \dfrac{V}{{{R_3}}}$
$ \Rightarrow \dfrac{1}{R} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}}$
Let's consider a special case of the resistances connected in parallel. In this case, the resistances are of the same value, that is $\dfrac{1}{{{R^/}}} = \dfrac{1}{R} + \dfrac{1}{R} + \dfrac{1}{R} = = > \dfrac{1}{{{R^/}}} = \dfrac{3}{R} = = > {R^/} = \dfrac{R}{3}$
Hence, the net resistance of the circuit becomes one-third the value of the resistance in each of the branches. Using the same formulation for $N$ branches, we get
${R_{net}} = \dfrac{R}{N}$-----🡪(1)
Where$(R)$is the resistance of each branch and $(N)$is the number of branches
For the current problem, we have multiple $176\Omega $ in parallel to each other. These
are connected to $220V$the line and the net current is $5A$ Hence using Ohm's law
and the value of resistance from the equation $(1)$, we get
$V = I{R_{net}} = = > 220 = 5(\dfrac{{176}}{N}) = = > N = (\dfrac{{176}}{{44}}) = = > N = 4$
Hence, 4 of the $176\Omega $resistors in parallel would be required to get a net current
of $5A$ flowing through a $220V$ line.
Note: It's important to remember that in a parallel resistance circuit connection, the voltage drawn by all the resistances is equal. An everyday example of this is the way electricity reaches all our houses. The constant $220V$ voltage is supplied to all the households in a locality since all the houses are in a parallel connection to each other.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE