A, B, C and D are four points in space and it is known that: 𝑉𝐴𝐵=8𝑉V AB =8V, 𝑉𝐵𝐷=−9𝑉V BD =−9V, 𝑉𝐶𝐴=13𝑉V CA =13V and the potential at A = 𝑉𝐴=−5𝑉V A =−5V. Using this information find the potential 𝑉𝐷V D at D
Question
A, B, C and D are four points in space and it is known that: 𝑉𝐴𝐵=8𝑉V AB =8V, 𝑉𝐵𝐷=−9𝑉V BD =−9V, 𝑉𝐶𝐴=13𝑉V CA =13V and the potential at A = 𝑉𝐴=−5𝑉V A =−5V. Using this information find the potential 𝑉𝐷V D at D
Solution
To find the potential at point D (V_D), we can use the given information about the potentials at points A, B, and C.
We know that the potential difference between two points is equal to the potential at the second point minus the potential at the first point.
So, we can write the potential at B (V_B) in terms of the potential at A (V_A) and the potential difference between A and B (V_AB):
V_B = V_A + V_AB V_B = -5V + 8V V_B = 3V
Next, we can write the potential at D (V_D) in terms of the potential at B (V_B) and the potential difference between B and D (V_BD):
V_D = V_B + V_BD V_D = 3V - 9V V_D = -6V
So, the potential at point D is -6V.
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