Three resistors R1=5ohms, R2=3ohms, and R3=4ohms are connected in series to each other. A voltmeter connected in parallel to resistor R2 measures voltage of 6V. What is the net voltage in the circuit?
the same current flows through all the resistors.
I = E2/R2 = 6/3 = 2 amps
Now E=IR across the other resistors.
Total voltage is the sum across all three R's.
To find the net voltage in the circuit, we need to calculate the total resistance first using the formula for resistors connected in series:
Total Resistance (RT) = R1 + R2 + R3
Substituting the given values, we have:
RT = 5Ω + 3Ω + 4Ω
RT = 12Ω
Since the voltmeter is connected in parallel to resistor R2, it measures the same voltage as the resistor. Thus, the voltage across resistor R2 is 6V.
To find the net voltage in the circuit, we can use Ohm's Law:
Voltage (V) = Current (I) × Resistance (R)
In this case, the current flowing through the circuit is the same, given that the resistors are connected in series. Therefore, we can equate the voltage across resistor R2 to the net voltage in the circuit:
6V = Current (I) × 3Ω
Solving for the current (I):
I = 6V / 3Ω
I = 2A
Now, we can find the net voltage by multiplying the current by the total resistance:
Net Voltage (V) = Current (I) × Total Resistance (RT)
Substituting the given values, we have:
V = 2A × 12Ω
V = 24V
Therefore, the net voltage in the circuit is 24V.
To find the net voltage in the circuit, we need to understand how resistors in series affect the flow of current and the voltage across each resistor.
When resistors are connected in series, the total resistance is the sum of the individual resistances. In this case, R1, R2, and R3 are connected in series, so the total resistance (RT) is given by:
RT = R1 + R2 + R3
= 5Ω + 3Ω + 4Ω
= 12Ω
Now, the voltage across each resistor in a series circuit is proportional to its resistance. So, we can find the voltage across each resistor using the formula:
Voltage across resistor = (Resistance of resistor / Total resistance) × Applied voltage
Given that the voltage across resistor R2 is 6V, and the resistance of R2 is 3Ω, we can solve for the applied voltage using the formula:
Applied voltage = (Voltage across resistor × Total resistance) / Resistance of resistor
Applied voltage = (6V × 12Ω) / 3Ω
= 72V / 3Ω
= 24V
Therefore, the net voltage in the circuit is 24V.