Question

2ohms
4ohms
4ohms connected in parallel
Calculate the total resistance in the circuit and the total current flowing in
the circuit.​

Answer 1

Answer:

The total resistance is 6 Ω and current in the circuit is 1 A.

Explanation:

The circuit consists of resistors of 2 Ω, 4 Ω, 4 Ω and 5 Ω

The resistors are connected in parallel.

• $\sf{R_1}$ = 2 Ω
• $\sf{R_2}$ = 4 Ω
• $\sf{R_3}$ = 4 Ω
• $\sf{R_4}$ = 5 Ω

________________________

Equivalent Resistance of resistors in parallel =

$\bigstar \: \boxed{\sf{ \dfrac{1}{R_P} = \dfrac{1}{R_1} +\dfrac{1}{R_2} +\dfrac{1}{R_3} }}$

$\sf{\longrightarrow} \: \dfrac{1}{R_P} = \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{4}$

$\sf{\longrightarrow} \: \dfrac{1}{R_P} = \dfrac{2 + 1 + 1}{4}$

$\sf{\longrightarrow} \: \dfrac{1}{R_P} = \dfrac{4}{4}$

$\sf{\longrightarrow} \: R_P = 1$

The equivalent resistance is the 3 resistors is 1 Ω

________________________

The resistors $\sf{R_{1,2,3}}$ and $\sf{R_4}$ are in series.

$\bigstar \: \boxed{{\sf{R_s = R_{1,2,3} \: + R_4}}}$

$\longrightarrow{\sf{R_s = 1 +5}}$

$\longrightarrow{\sf{R_s =6}}$

Total resistance of the circuit is 6 Ω

________________________

Total current in the circuit =

Following the Ohm's Law,

$\bigstar \: \boxed{\sf{V = I \times R}}$

• V = 6 V
• I = ??
• R = 6 Ω

$\sf{\longrightarrow} \: 6 = I \times 6$

$\sf{\longrightarrow} \: 6 = 6I$

$\sf{\longrightarrow} \:I = \dfrac{6}{6}$

$\sf{\longrightarrow} \:I = 1$

Current = 1 A

Therefore, the total resistance is 6 Ω and current in the circuit is 1 A.

Answer 2

Answer:

Given :-

2ohms

4ohms

4ohms connected in parallel

To Find :-

The resistance in the circuit and the total current flowing in the circuit.

Solution :-

Since they are in parallel

So

1/Rn = 1/R1 + 1/R2 + 1/R3

1/Rn = 1/2 + 1/4 + 1/4

1/Rn = 2(1) + 1 + 1/4

1/Rn = 2 + 1 + 1/4

1/Rn = 4/4

4(1) = 4(Rn)

4 = 4Rn

4/4 = Rn

1 = Rn

Now

R4 is in series

Rn = R1,2,3 + R4

Rn = 1 + 5

Rn = 6 Ω

Now

I = V/R

I = 6/6

I = 1 A