First, we need to find the total resistance of the circuit. In order to find the total resistance of the circuit, we need to combine all of the parallel resistors first, then add them together as resistors in series.

Combine  with :

Combine  with :

Combine  with :

Then, add the combined resistors, which are now all in series: 

Then, we will need to use Ohm's law to determine the total current of the circuit.

Combine all of our voltage sources:

Plug in our values:

We know that the voltage drop across parallel resistors must be the same, so:

Use Ohm's law:

We also know that:

Substitute:

Solve for :

Plug in our values, we get 

Use: 

First, we need to find the total resistance of the circuit. In order to find the total resistance of the circuit, we need to combine all of the parallel resistors first, then add them together as resistors in series.

Combine  with :

Combine  with :

Combine  with :

Then, add the combined resistors, which are now all in series: 

Then, we will need to use Ohm's law to determine the total current of the circuit.

Combine all of our voltage sources:

Plug in our values:

We know that the voltage drop across parallel resistors must be the same, so:

Use Ohm's law

We also know that:

Substitute: 

Solve for :

Plug in our values, we get 

Use

The first step is to find the total resistance of the circuit.

In order to find the total resistance of the circuit, it is required to combine all of the parallel resistors first, then add them together as resistors in series.

Combining with ,  with ,  with .

Then, combining  with  and :

Ohms is used law to determine the total current of the circuit

Combing all voltage sources for the total voltage.

Plugging in given values,

 The voltage drop across parallel resistors must be the same, so:

Using ohms law:

It is also true that:

Using Subsitution

Solving for :

Plugging back into ohms law in order to find the voltage drop.

 .

Since each resistor is in parallel, the voltage drop across each will be .

Since each resistor is identical, they all have the same resistance.

Using

and

It is determined that

Since each resistor is in parallel, the voltage drop across each will be .

Since each resistor is identical, they all have the same resistance.

Using

and

It is determined that

Using

 for all three resistors

The first step to solving this problem is to try to simplify it. We can combine resistors  and  into one equivalent resistance:

Now, we have a single loop with multiple circuit components all connected in series. To calculate the current going through this loop, we need to use Kirchoff's loop law, which says that the sum of all the voltages in a single loop is equal to 0.

This may look confusing at first. Starting from the bottom left point in the circuit, let's begin to go around the loop. The voltage on the battery is +12. The voltage of the resistor is  from Ohm's law  and since voltage is lost, it's negative.

Continuing on to the capacitor, the voltage across it is , and is negative because voltage is lost across it. 

Finally, on to the equivalent resistor, the voltage across it is .

Plugging in all the numbers from the problem and solving the equation above for  gives us 

Our first step in solving this circuit is to find the equivalent resistance of  and . If you have two elements in parallel (whether they be resistors, capacitors, or inductors), an easy way to do this is

This is the same as the following equation, which may look more familiar; however, the first equation only works for two elements.

Now that we have the equivalent of the two resistances, we can combine it in series with  to get the total .

Now that we have the total resistance, we can combine it with the total voltage given in the problem and use Ohm's law to calculate the current.

The key to solving this problem is to recognize the structure of the circuit. The voltage source, the capacitor, and the two resistors are in parallel to each other, meaning that they have the same voltage! This is a very important concept and will make many problems easier to solve.

Since the branch containing the two resistors has 5V, we can easily solve for the voltage of .

One easy way to solve for the voltage is to calculate the current going through the entire branch. Keep in mind here that two resistors in series have the same current.

Now that we have the current that flows through each of the two resistors, we can calculate the voltage drop across only the first resistor.

A represents a battery. Convention dictates that the direction of charge flow is from the small side to the large side. B is a resistor. Its symbol makes sense if you view the flow of electrons similarly to water flowing; water's flow is resisted by turns, so the jagged lines would evoke that thought for electrons flowing. C is a capacitor. Common capacitors are parallel plates of equal surface area separated by a vacuum or dielectric. This is why the lines are equal in length, unlike the battery. D is a solenoid. A solenoid is a coil of wire that induces a magnetic inside of it.

The time constant of this RC circuit is only dependent on the value of the resistance and the capacitor, not the voltage source.