A30-μf capacitor is charged to 80 v and then connected across an initially uncharged capacitor of unknown capacitance c. if the final potential difference across the 30-μf capacitor is 20 v, determine c.

90 μF

Explanation:

C' = Capacitance of charged capacitor = 30 x 10⁻⁶ F

= initial potential difference across the plates = 80 V

= final potential difference across the plates = 20 V

Q = Charge stored by unknown capacitance

Charge stored by unknown capacitance is given as

Q = C' ( - )

Q = (30 x 10⁻⁶) (80 - 20)

Q = 1.8 x 10⁻³ C

C = Capacitance of unknown capacitor

V = Potential difference across the plates of unknown capacitor = 20

Charge stored by unknown capacitor is given as

Q = CV

1.8 x 10⁻³ = C (20)

C = 90 x 10⁻⁶ F

C = 90 μF

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.