A student builds the circuit as shown in the diagram. He uses a resistance of
3ohm each for R1, R2 and R3 with battery of 2 Volt as shown in the diagram
given below. Calculate the current through the circuit
Answers
Answer:-
- Current, I = 4A
Step-by-step explanation:
Given : Resistance of each resistor is 3Ω and potential difference across terminals of battery is 2v.
To find : Current in the circuit
Solution :
Here in this question, concept of ohm's law is used. We are Given a circuit and we are asked to find current in the whole circuit. We are given with the potential difference of battery and resistance of the resistors which are connected in the circuit. Firstly we have to find the equivalent resistance of circuit so that we could apply ohm's law to find current. So let's proceed with finding equivalent resistance in circuit !
We can see in the given figure that resistors R₁ and R₂ are in series connection.
Resistance in series connection can be expressed as::
→ R = R₁ + R₂ + R₃...
Substitute value of resistors
→ R = R₁ + R₂
→ R = 3Ω + 3Ω
→ R =6Ω
Now we can see that the connection of R₁ and R₂ is in parallel connection with resistor R₃.
Resistance in parallel connection can be expressed as::
→ 1/Rₙ = 1/R₁ + 1/R₂ + 1/R₃...
Substitute values
→ 1/Rₙ = 1/R₁ + 1/R
→ 1/Rₙ = 1/6Ω + 1/3Ω
→ 1/Rₙ = (1+2)/6Ω
→ 1/Rₙ = 3/6Ω
→ 1/Rₙ = 1/2Ω
→ Rₙ =2Ω
So the equivalent resistance in whole circuit is 2Ω.
Now we have ohm's law, according to which::
Potential difference is equal to product of current and resistance.
Or,
→ V = IR
Substituting value of resistance and voltage
→ V = IRₙ
→ 2v = I(2Ω)
→ 2v(2Ω) = I
→ 4 Volt. ohm = I
→ 4 Ampere = I
So the current flowing through whole circuit is 4A.
★ Terms used by me in solution:-
- I = Current in whole circuit
- V = Potential created by battery
- R = Resistance of connection of R₁ and R₂
- Rₙ = Equivalent resistance of whole circuit
★ More formula:-
- H = I²Rt
- P = VI
- P = V²/R
- I = Q/t
- P = W/t
- I = w/Q
- H = VIt
- H = V²t/R