Since the resistors are in parallel to a  battery, the voltage drop across each resistor has to be equal to the voltage gain across the battery. Therefore, the voltage drop for any of the resistors will be .

In order to find the equivalent resistance of resistors in parallel, we add the inverses of their values, as shown below

Finally 

We can answer this by looking at how the equivalent resistance of a parallel circuit is calculated.

.

What we can see is that because the inverses are being added, any additional resistors will make contributions to the denominator of the fraction. Thus, lowering, or decreasing the equivalent resistance of the circuit.

The equivalent resistance of resistors in series is calculated by , while for parallel resistors, . This clearly shows that resistors in a series configuration will generate a much higher, or maximum, equivalent resistance value.

In this question, we're presented with a circuit diagram. We're told the values of the voltage source as well as each of the three resistors. We're asked to find the current that is flowing through resistor B.

To begin this problem, we'll need to figure out how much current is flowing through the entire circuit. But before we can do this, we'll need to figure out what the equivalent resistance of the circuit is. To do this, we'll need to look at how the circuit is configured so that we can see which resistors are in series, and which are in parallel.

We can see that resistors A and B are in parallel with each other. Furthermore, both A and B are in series with resistor C. So to begin, we'll need to find the equivalent resistance for resistors A and B. Using the equation for parallel resistors, we can calculate the equivalent resistance for resistors A and B.

Now that we've found the equivalent resistance for A and B, we can use this value in combination with resistor C, which is connected in series.

Because we've considered all the resistors in the circuit, this value is the total resistance of the circuit. Now, we can use Ohm's law in order to find the current running through the circuit.

Now that we have the total amount of current flowing through the circuit, we can look at each individual resistor in order to determine the amount of current flowing through that resistor. We can see that after traveling past the voltage source, there is a node that branches off, leading to resistor A and B. Because each of these resistors has the same resistance, the current through each must also be the same. Therefore, the current will split in half at the node, causing half the current to go to resistor A, and the other half to go to resistor B. Thus, the current flowing through resistor B is .

In this question, we're presented with a circuit that has a number of resistors connected in series and in parallel, and we're asked to find the total resistance of the circuit.

In looking at this diagram, the first thing that we need to do is find the equivalent resistance for each group of resistors that are connected in series, which is the top two rows. And remember, resistors add directly when arranged in series.

Then, we can do the same thing for the middle row.

Now that we have a value of resistance for each row, we can now consider all three rows together as being connected in parallel. Remember, resistors arranged in parallel will add inversely.

In order to find the equivalent resistance, you must take small steps and slowly work towards finding the total equivalent resistance.You can combine resistors if they are in parallel. The expression to find parallel equivalent resistance is:

You can also combine resistors in series, or one after the other. The expression to find resistors in series is:

To start off, you can combine R2 and R3, since they are both in parallel:

Next, you can combine some of the series resistors together. 

After this, you can combine the following resistors in parallel:

Then, combine  and  in series:

Now get rid of the last parallel by combining  and  in parallel:

Now finally, add the remaining resistors in series to find the equivalent resistance:

The goal of this question is to realize that when two resistors are connected in parallel, the equivalent resistance is lower than either of the two original resistors. But when two resistors are connected in series, the equivalent resistance is the sum of the two original resistors. Therefore to minimize our equivalent resistance, we want all the resistance to be in the parallel resistors, leaving  for the resistor in series.

When resistors are in series, they add normally, such as

when in series, they add via their reciprocal

Using these rules, we can first combine all the resistors in series ( and ,  and ), which can be diagrammed as such:

Using the parallel rule, find to total equivalent resistance.

The relationship between a capacitor's charge and the voltage drop across it is:

Since the voltage drop across both  and  are the same, we just have to worry about the right part of the circuit. Capacitors are the opposite of resistors when it comes to finding equivalent capacitance, so for capacitors in series the two capacitors on the right will add as such

Plugging into the first equation.

Since the two capacitors are in series they must share the same charge as the equivalent capacitor.