A resitor of unknown resistance and a 35-omega resistor are connected across a 120-V emf device in such a way that an 11-A current flows. What is the value of the unknown reisistance?
13 years ago
11 months ago
To determine the value of the unknown resistance in this circuit, we can apply Ohm's Law and Kirchhoff's Laws. Here's how you can calculate it step by step:
Step 1: Write down the given values:
- Voltage (emf) across the circuit (V_emf) = 120 V
- Known resistance (R2) = 35 Ω
- Current flowing through the circuit (I) = 11 A
Step 2: Apply Ohm's Law:
Ohm's Law states that the voltage across a resistor is equal to the current flowing through it multiplied by its resistance.
V = I * R
In this case, we can apply Ohm's Law to the known resistance (R2):
V_R2 = I * R2
Step 3: Substitute the known values:
V_R2 = 11 A * 35 Ω
V_R2 = 385 V
Step 4: Apply Kirchhoff's Laws:
Kirchhoff's Voltage Law (KVL) states that the sum of voltages around a closed loop in a circuit should be zero.
In this circuit, the total voltage (emf) across the circuit is equal to the sum of the voltages across the individual resistances:
V_emf = V_R1 + V_R2
Step 5: Substitute the known values:
V_emf = V_R1 + 385 V
V_emf = 120 V
Step 6: Solve for the unknown resistance:
Rearrange the equation from Step 5 to isolate the unknown resistance (R1):
V_R1 = V_emf - V_R2
R1 = (V_emf - V_R2) / I
Substitute the known values:
R1 = (120 V - 385 V) / 11 A
R1 = -265 V / 11 A
R1 ≈ -24.1 Ω
Since resistance can't be negative, it seems like there's an error in the calculations or setup of the circuit.
Double-check the calculations and the information provided to ensure accuracy.