Exhibit 32.a

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, each of the undersigned officers of Dominion Resources, Inc. (the “Company”), certify that:

1. the Quarterly Report on Form 10-Q for the quarter ended March 31, 2012 (the “Report”) of the Company to which this certification is an exhibit fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m(a) or 78o(d)).

2. the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company as of March 31, 2012 and for the period then ended.

/s/ Thomas F. Farrell II

Thomas F. Farrell II

President and Chief Executive Officer

April 26, 2012

/s/ Mark F. McGettrick

Mark F. McGettrick

Executive Vice President and Chief Financial Officer

April 26, 2012