Question

Consider the circuit shown in the figure below. (Let R = 30.0 ?.)

Consider the circuit shown in the figure below. (Let R = 30.0 Ω.) 25.0 V 10.0 Ω 10.0 Ω 5.00 Ω 5.00 Ω (a) Find the current in the 30.0-2 resistor. Enter a number. otential difference across the 10-Ω resistor, the 5-Ω resistor and the (R + 5-Q) resistor combination, what can you conclude about these resistors? A (b) Find the potential difference between points a and b

(a) Find the current in the 30.0-? resistor.

(b) Find the potential difference between points a and b.

Answer 1

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Let the potential at point b is 25 v-1 at point a is x v and at point c = y v Total current through point a = 0 x - y/5 + x - 0/10 + x - 25/10 + x - 25/5 = 0 2x - 2y + x + x - 25 + 2x - 25/10 = > 6x - 2y = 50 = > 3x - y = 25 ...(1) similarly for point b, 25 - y/30 + 25 - x/10 + 25 - x/5 + 0 - x/10 = 0 = > 25 - y + 75 - 3x + 150 -6x - 3x/30 =0 = > 12x + y = 250...(2) solving eq(1) and eq(2) x = 18.33 v & y = 30 v a) current in 30 ohm resistor, I_R = y - 25/30 = 30 - 25/30 = 5/30 = 0.167 A b) potential difference between points a and b, v_ba = v_b - v_a = 25 - x = 25 - 18.33 = 6.67 v