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: Consider the voltage across resistor R 2 as V 1 . Since, in parallel circuits the potential difference ( V 1 ) remains the same, so the across resistors R 1 , R 3 and R 4 will be same that is 10 V. Consider the current in resistor R 3 as I 3 . Current in the resistor R 3 can be found out by Ohm’s law is as follows. Substitute I 3 for I , R 3 for R and V 1 for E in equation (1) to obtain the expression for current. V 1 = I 3 R 3 I 3 = V 1 R 3 Substitute 10 V for V 1 and 4 Ω for R 3 to obtain the value of I 3 . I 3 = 10 V 4 Ω I 3 = 2.5 A Consider the current in resistor R 1 as I 1 . Current in resistor R 1 can be found out by Ohm’s law is as follows. Substitute I 1 for I , R 1 for R and V 1 for E in equation (1) to obtain the expression for current. V 1 = I 1 R 1 I 1 = V 1 R 1 Substitute 10 V for V 1 and 20 Ω for R 1 to obtain the value of I 1 . I 1 = 10 V 20 Ω = 0.5 A Current in the series circuit is same in all the components, so the current in resistor R 6 is same as the current in resistor R 5 , that is, 5 A which is also the battery current ( I ). The current through resistor R 2 is the remaining current form the source current, that is the difference between the source current and the summation of current through the resistors R 1 , R 3 and R 4 Consider the current through resistor R 2 as I 2 . I 2 = I − ( I 1 + I 3 + I 4 ) Substitute 5 A for I , 0.5 A for I 1 , 2.5 A for I 3 , and 1 A for I 4 to compute the current through the resistor R 2 . I 2 = 5 A − ( 0 .5 A + 2.5 A+1 A ) = 1 A Value of resistor R 2 is calculated as follows. Substitute R 2 for R total , I 2 for I and V 1 for E in equation (1) to obtain the expression for value of resistor R 2 . V 1 = I 2 R 2 R 2 = V 1 I 2 Substitute 10 V for V 1 and 1 A for I 2 to compute the resistance R 2 . R 2 = 10 V 1 A = 10 Ω The value of resistor R 4 is calculated as follows

11th Edition

ISBN: 9780134159386

Author: Dale Ewen, Neill Schurter, Erik Gundersen

Publisher: PEARSON

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Chapter 17.10, Problem 11P

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Solution Summary: The author explains the formula for Ohm's law: E is potential difference, I is current, and R is resistance. The current in the resistor R_3 can be found out by Oh

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Chapter 17 Solutions