Finding the equivalent resistance, total power supply, and emf of the battery, in a given circuit.

Question

In the circuit in the image attached below,

https://ibb.co/vhBSs3z

where R₁=3Ω, R₂=10Ω, R₃=5Ω, R₄=4Ω, R₅=3Ω

How do I find

a) the equivalent resistance for this circuit

b) If the total power supplied to the circuit is 4W

c) the emf of the battery

Answer 1

Answer 2

R2 and R3 are in parallel, so they could be combined into a resistor which we can all R23. R23 and R4 are in series, so they can be combined in one resistor called R234. R234 and R5 are in parallel; they an be combined into a resistor called R2345. Finally R1 and R2345 are in series , and they can be combined into one final resistor that we can call R.

Power = I²R so I = Sq RT (4² / R). E = IR.

You can do the math.

Answer 3

Step 1: Analyze the Circuit Configuration

Based on the diagram:

1. Resistors R2​ (10 Ω) and R3(5 Ω) are in parallel.
2. Their equivalent resistance is then in series with R4​ (4 Ω).
3. This combined series-parallel network is in parallel with R5​ (3 Ω).
4. Finally, this entire network is in series with R1​ (3 Ω) and connected to a battery with emf E.

Let's go through the calculations step-by-step.

Step 2: Calculate the Equivalent Resistance for R2​ and R3

Since R2​ and R3 are in parallel, their equivalent resistance R23​ is given by:

1/R23 = 1/R2+1/R3 = 1/10 + 1/5

 R23 =

Step 3: Add R4​ in Series with R23

Now, we add R4 (4 Ω) in series with R23​:

R234=R23+R4=

Step 4: Calculate the Parallel Combination of R234​ with R5

Next, R234 is in parallel with R​ (3 Ω), so we find their equivalent resistance R2345​:

1/R2345 = 1/R234 + 1/R5 =

R2345 = 1/ (1/R234 + 1/R5)

Step 5: Add R1​ in Series with R2345R

Finally, R1 (3 Ω) is in series with R2345​, so the total equivalent resistance Req is:

Req=R1+R2345= Equivalent Resistance

The equivalent resistance of the circuit is:

Req =

Step 6: Determine the Total Power Supply (if current or voltage is known)

We would need the current I or the emf E of the battery to calculate the total power supplied.

If the emf E is known:

I = E/Req

Ptotal = E * I = E²/Req

If the current I is known:

Ptotal = I² * Req

Summary:

1. Equivalent Resistance Req=
2. Total Power Supply: Requires either E or I

To best visualize redraw the circuit after each step 2, 3, 4, and 5.