Explanation Formula used: Write the expression for Ohm’s law. E = I R total (1) Here, E is potential difference. I is the current. R total is the total resistance. Calculation: Refer to Table in Question 8P for the values of potential differences, resistances and current. Potential difference across R 1 and R 2 are equal since they are connected in parallel. So, the potential difference across R 2 is 6 V. Potential difference across R 4 and R 5 are equal since they are connected in parallel. So, the potential difference across R 4 is 8 V. The resistances R 1 , R 2 and R 4 can be obtained by Ohm’s law. Substitute R 1 for R , V 1 for E and I 1 for I in equation (1) to obtain the expression for value of resistance. V 1 = I 1 R 1 R 1 = V 1 I 1 Substitute 6 V for V 1 and 3 A for I 1 to compute the resistance. R 1 = 6 V 3 A = 2 Ω Substitute R 2 for R , V 2 for E and I 2 for I in equation (1) to obtain the expression for value of resistance. V 2 = I 2 R 2 R 2 = V 2 I 2 Substitute 6 V for V 1 and 2 A for I 1 to compute the resistance. R 2 = 6 V 2 A = 3 Ω Substitute R 4 for R , V 4 for E and I 4 for I in equation (1) to obtain the expression for value of resistance. V 4 = I 4 R 4 R 4 = V 4 I 4 Substitute 6 V for V 4 and 3 A for I 4 to compute the resistance. R 4 = 8 V 1 A = 8 Ω The total current in the circuit is the summation of all the currents through any resistances connected in parallel, since in series the current remains the same. I = I 1 + I 2 Substitute 3 A for I 1 and 2 A for I 2 to compute the total current. I = 3 A + 2 A = 5 A The resistance of the circuit can be found by Ohm’s law. Substitute 5 A for I and 30 V for E in equation (1) to compute the net resistance. 30 V = 5 A × R total R total = 30 V 5 A R total = 6 Ω Potential difference across resistor R 3 can be found by Ohm’s law. Substitute R 3 for R and V 3 for V in equation (1) to obtain the expression for current. V 3 = I R 3 Substitute 5 A for I and 3 Ω for R 3 to compute the potential difference across resistor R 3

11th Edition

ISBN: 9780134159386

Author: Dale Ewen, Neill Schurter, Erik Gundersen

Publisher: PEARSON

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Chapter 17.10, Problem 8P

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Solution Summary: The author explains the formula used to calculate Ohm's law: E is potential difference, I is the current, and R_total is total resistance.

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Chapter 17 Solutions