Aseries circuit contains a generator to devices and connecting wires the resistance of the two devices are 15 ohms and 10 ohms the voltage supplied by the generator is 75 volts what will be the voltage drop in the device with 10 ohms of resistance
The Correct Answer and Explanation is:
Correct Answer:
The voltage drop across the device with 10 ohms of resistance is 30 volts.
Step-by-Step Solution and Explanation:
In a series circuit, the same current flows through all the components. The voltage supplied by the generator is divided among the components based on their resistance values. The formula for calculating voltage drop across a specific resistor in a series circuit is:V=I×RV = I \times RV=I×R
Where:
- VVV is the voltage drop across the resistor
- III is the current flowing through the circuit
- RRR is the resistance of the device
Step 1: Calculate the total resistance
The total resistance RtotalR_{total}Rtotal in a series circuit is simply the sum of individual resistances:Rtotal=R1+R2=15 Ω+10 Ω=25 ΩR_{total} = R_1 + R_2 = 15\ \Omega + 10\ \Omega = 25\ \OmegaRtotal=R1+R2=15 Ω+10 Ω=25 Ω
Step 2: Calculate the total current using Ohm’s Law
Ohm’s Law states:V=I×RV = I \times RV=I×R
Rearrange to solve for current:I=VR=75 V25 Ω=3 AI = \frac{V}{R} = \frac{75\ V}{25\ \Omega} = 3\ AI=RV=25 Ω75 V=3 A
Step 3: Calculate the voltage drop across the 10-ohm resistorV=I×R=3 A×10 Ω=30 VV = I \times R = 3\ A \times 10\ \Omega = 30\ VV=I×R=3 A×10 Ω=30 V
Final Answer: The voltage drop across the 10-ohm device is 30 volts
Explanation:
In a series circuit, all components share the same current. However, the voltage supplied by the generator is divided among the components based on their resistance. The component with higher resistance will experience a larger voltage drop, while the one with lower resistance will have a smaller voltage drop.
In this problem, the two devices have resistances of 15 ohms and 10 ohms, respectively. The total resistance is the sum of both, making it 25 ohms. Using the supplied voltage of 75 volts and applying Ohm’s Law, the current is found to be 3 amperes throughout the circuit.
Finally, multiplying the current by the resistance of the second device (10 ohms) gives a voltage drop of 30 volts across that device. This demonstrates how voltage is distributed in a series circuit according to each component’s resistance.
