A 15-V battery is hooked up to three resistors in series. The voltage drop across the first resistor is 3V and the voltage drop across the sencond resistor is 10V. What is the voltage drop across the last resistor?
I don't understand what equation to do for this problem. Thanks.
E = V1+V2+V3 = 15.
V1 = 3 Volts.
V2 = 10 Volts.
V3 = ?.
Well, if you want to be serious about it, you can use Kirchhoff's Voltage Law (KVL). According to KVL, the sum of the voltage drops across all the elements in a closed loop should equal the source voltage.
So, in this case, you can set up the equation like this:
3V + 10V + ?V = 15V
Now solve for the missing voltage drop. But before you do that, let me add a little humor to the equation:
"If the first resistor is feeling a little voltage drop, and the second resistor is feeling 10V, it's time for the last resistor to step up and show some electric potential. After all, it's charged with the responsibility to balance the equation!"
Okay, back to business. Solving the equation:
3V + 10V + ?V = 15V
13V + ?V = 15V
?V = 15V - 13V
?V = 2V
So, the voltage drop across the last resistor is 2V. Now go tell that resistor to embrace its electric potential!
To find the voltage drop across the last resistor, you can use Kirchhoff's Voltage Law (KVL). According to KVL, the sum of the voltage drops in a closed loop must be equal to the total voltage applied.
In this case, the total voltage applied is 15V, and the voltage drops across the first and second resistors are 3V and 10V, respectively. To find the voltage drop across the last resistor, you subtract the sum of the voltage drops across the other two resistors from the total voltage.
Let's call the voltage drop across the last resistor V3. Using KVL, we can write the equation:
V1 + V2 + V3 = Total voltage
Substituting in the given values, we get:
3V + 10V + V3 = 15V
Simplifying the equation gives:
13V + V3 = 15V
To isolate V3, we subtract 13V from both sides:
V3 = 15V - 13V
Therefore, the voltage drop across the last resistor is 2V.
To understand how to solve this problem, let's start with the basic concept of voltage in a series circuit.
In a series circuit, the total voltage provided by the battery is divided across the individual resistors. The sum of the voltage drops across the resistors should equal the total voltage provided by the battery.
In this case, we have a 15V battery connected to three resistors in series. Let's call the three resistors R1, R2, and R3.
According to the problem, the voltage drop across the first resistor (R1) is 3V, and the voltage drop across the second resistor (R2) is 10V. We need to find the voltage drop across the last resistor (R3).
To find the voltage drop across R3, we first need to find the total voltage drop across R1 and R2. This can be done by subtracting the voltage drops across R1 and R2 from the total voltage provided by the battery.
Total voltage drop across R1 and R2 = Voltage provided by the battery - Voltage drop across R1 - Voltage drop across R2
So, the total voltage drop across R1 and R2 = 15V - 3V - 10V = 2V
Since the series circuit has a constant voltage drop across each resistor, we can conclude that the voltage drop across the third resistor (R3) is also 2V.
Therefore, the voltage drop across the last resistor (R3) is 2V.