Question

For the network shown below, the value of V_B– V_A is ________V.

Answer 1

Correct Answer: 10

To solve for V_B - V_A in the given circuit, we analyze the circuit using Ohm's Law and the principles of series circuits.

The circuit consists of a 15 V battery and two resistors, 1 Ω and 2 Ω, in series.

Step-by-step Calculation:

1. Calculate the total resistance in the circuit:
   R_total = 1 Ω + 2 Ω = 3 Ω
2. Determine the current flowing through the circuit using Ohm's Law, V = IR:
   I = V / R_total = 15 V / 3 Ω = 5 A
3. Find the voltage drop across the 2 Ω resistor using V = IR:
   V_drop = I × 2 Ω = 5 A × 2 Ω = 10 V
4. Since the direction of current flow is from A to B, the potential difference V_B - V_A is given by the negative of the voltage drop across the 2 Ω resistor:
   V_B - V_A = -10 V

Verification:

The calculated value is -10 V, which falls within the expected range of 10 to 10 V.

Thus, V_B - V_A = -10 V.