An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Substitute each value of n (1 to 5) into the formula P = 1 + ( n − 1 ) ( 2 ) .
Calculate the corresponding value of P for each n .
Match the calculated pairs ( n , P ) with the given options.
The correct option is C) ( 1 , 1 ) , ( 2 , 3 ) , ( 3 , 5 ) , ( 4 , 7 ) , ( 5 , 9 ) .
Explanation
Understanding the Problem The problem provides a formula to calculate the number of notebooks, P , awarded to students based on their ranking, n , from 1st to 5th place. The formula is P = 1 + ( n − 1 ) ( 2 ) . We need to determine which of the given options correctly matches the rank n with the number of notebooks P .
Solution Plan We will substitute n = 1 , 2 , 3 , 4 , 5 into the formula P = 1 + ( n − 1 ) ( 2 ) to find the corresponding values of P .
Calculating Notebooks for Each Place For n = 1 (5th place): P = 1 + ( 1 − 1 ) ( 2 ) = 1 + 0 = 1 For n = 2 (4th place): P = 1 + ( 2 − 1 ) ( 2 ) = 1 + 1 ( 2 ) = 1 + 2 = 3 For n = 3 (3rd place): P = 1 + ( 3 − 1 ) ( 2 ) = 1 + 2 ( 2 ) = 1 + 4 = 5 For n = 4 (2nd place): P = 1 + ( 4 − 1 ) ( 2 ) = 1 + 3 ( 2 ) = 1 + 6 = 7 For n = 5 (1st place): P = 1 + ( 5 − 1 ) ( 2 ) = 1 + 4 ( 2 ) = 1 + 8 = 9
Identifying the Correct Option So, the correct series of pairs ( n , P ) is ( 1 , 1 ) , ( 2 , 3 ) , ( 3 , 5 ) , ( 4 , 7 ) , ( 5 , 9 ) . Comparing this with the given options, we find that option C matches our calculated series.
Final Answer Therefore, the correct answer is C) ( 1 , 1 ) , ( 2 , 3 ) , ( 3 , 5 ) , ( 4 , 7 ) , ( 5 , 9 ) .
Examples
Imagine you're organizing a school competition and want to reward the top participants. The formula P = 1 + ( n − 1 ) ( 2 ) helps you determine how many prizes (like notebooks) each winner gets based on their rank. For example, the first-place winner gets 9 notebooks, while the fifth-place winner gets only 1. This ensures a fair distribution of rewards, motivating students to strive for higher ranks. Understanding such formulas can help in various real-life scenarios, such as resource allocation, setting performance-based incentives, or designing tiered reward systems.
To find the number of electrons flowing through an electric device providing a current of 15.0 A for 30 seconds, we first calculate the total charge as 450 coulombs. We then use the charge of a single electron (approximately 1.6 x 10^(-19) coulombs) to find the number of electrons, resulting in approximately 2.81 x 10^{21} electrons flowing during this time period.
;
