How to combine two resistors with a voltage source

Question

^{simulate this circuit – Schematic created using CircuitLab}

^{simulate this circuit}

Are these two circuits the same? If not, could you please indicate why as well?

Answer 1

When starting out, your brain is easily tricked by the arrangement in which things are drawn rather than what they actually are. Side-by-side doesn't automatically mean parallel.

What if I took your "parallel" circuit:

^{simulate this circuit – Schematic created using CircuitLab}

and just changed it to this. Does it still look like it is in parallel to you? Or series for that matter? Remember, the current can flow into the circuit on those stubs from outside.

^{simulate this circuit}

• Parallel = voltage across all components are the same
• Series = current through all components is the same

Don't be tricked by how things are arranged on a page.

Answer 2

^{simulate this circuit – Schematic created using CircuitLab}

Figure 1. Whatever way you draw it it's a series circuit and the total resistance is R1 + R2.

^{simulate this circuit}

Figure 2. R1 and R2 are in parallel in this case.

Answer 3

There is a good way to understand either a combination is series or parallel. For example, take a look at the circuit below.

^{simulate this circuit – Schematic created using CircuitLab}

The left side of R₁ is directly connected to the positive terminal of the battery. Let's say the voltage is V_a. Same as this, the right side of R₁ is connected to the negative terminal of the battery. Let's say the voltage is V_b.

So the potential difference across R₁ is (V_a - V_b)
Similarly voltage across R₂ will also be (V_a - V_b)

If two resistors are parallel, then they will have the same potential difference between their terminals.

^{simulate this circuit}

Now for this new circuit, the upper side of the resistor R₁ is directly connected to the positive terminal of the battery. The voltage of that terminal is labeled as V_a.

Now there will be a voltage drop caused by the resistor R₁ (N.B. Ohm's law V=IR). So a new voltage level V_c will appear at the lower side of R₁. And the lower side of R₂ is directly connected to the negative terminal of the battery, which is labeled as V_b.

All series combination will cause this type of voltage change.

Let's take a complicated example.

^{simulate this circuit}

Just by inspection, it's quite difficult to understand. But if the node voltages are marked, then you will see that all of them have the same potential difference, which is (V_a - V_b). This means that they are all parallel to each other.

Answer 4

Sometimes, when you're still new to all this, it just isn't clear if two circuit elements are parallel (or series) connected.

If you're not sure, there's an easy 'trick' to test whether or not the two resistors are parallel connected: consider setting one of the resistors to zero ohms.

For example, set \$R_1=0\Omega\$ (essentially, replace \$R_1\$ with a wire).

It's clear that the voltage source sees the resistor \$R_2\$ as the load.

But this wouldn't be the case if \$R_1\$ and \$R_2\$ are parallel connected since, with \$R_1=0\$, we have

$$R_1||R_2 = \frac{0\cdot R_2}{0 + R_2} = 0\Omega$$

That is, zero ohms in parallel with \$R\$ ohms equals zero ohms.

Since the source doesn't see zero ohms with \$R_1=0\Omega\$, it follows that the two resistors are not parallel connected.

Answer 5

Maybe your confusion comes from the Thevenin equivalent circuit of the one you show (the voltage source Vth=V*R2/(R1+R2) in series with the resistor Rth=R1//R2). but you don't have to short circuit the output.

Answer 6

These are two different circuits because in first circuit the current is same throughout the circuit but in 2nd circuit if we place R1and R2 in parallel than current is divide between the resistors by the rule of KCL.